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Reconstruction of the solution of inverse Sturm–Liouville problem Bound. Value Probl. (IF 1.7) Pub Date : 2024-04-19 Zhaoying Wei, Zhijie Hu, Yuewen Xiang
In this paper we are concerned with an inverse problem with Robin boundary conditions, which states that, when the potential on $[0,1/2]$ and the coefficient at the left end point are known a priori, a full spectrum uniquely determines its potential on the whole interval and the coefficient at the right end point. We shall give a new method for reconstructing the potential for this problem in terms
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Finite-time blowup for the 3-D viscous primitive equations of oceanic and atmospheric dynamics Bound. Value Probl. (IF 1.7) Pub Date : 2024-04-11 Lin Zheng
In this paper, we prove that for certain class of initial data, the corresponding solutions to the 3-D viscous primitive equations blow up in finite time. Specifically, we find a special solution to simplify the 3-D systems, assuming that the pressure function $p(x,y,t)$ is a concave function. We also consider the equations on the line $x=0$ , $y=0$ .
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A comprehensive study on Milne-type inequalities with tempered fractional integrals Bound. Value Probl. (IF 1.7) Pub Date : 2024-04-10 Wali Haider, Hüseyin Budak, Asia Shehzadi, Fatih Hezenci, Haibo Chen
In the framework of tempered fractional integrals, we obtain a fundamental identity for differentiable convex functions. By employing this identity, we derive several modifications of fractional Milne inequalities, providing novel extensions to the domain of tempered fractional integrals. The research comprehensively examines significant functional classes, including convex functions, bounded functions
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Inverse source problem for the pseudoparabolic equation associated with the Jacobi operator Bound. Value Probl. (IF 1.7) Pub Date : 2024-04-09 Bayan Bekbolat, Niyaz Tokmagambetov
In this paper, we investigate direct and inverse problems for time-fractional pseudoparabolic equations associated with the Jacobi operator. The existence and uniqueness of the solutions are proven. Also, the stability result of the inverse source problem (ISP) is established.
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Multiplicity and nonexistence of positive solutions to impulsive Sturm–Liouville boundary value problems Bound. Value Probl. (IF 1.7) Pub Date : 2024-04-08 Xuxin Yang, Piao Liu, Weibing Wang
In this paper, we study the existence, nonexistence, and multiplicity of positive solutions to a nonlinear impulsive Sturm–Liouville boundary value problem with a parameter. By using a variational method, we prove that the problem has at least two positive solutions for the parameter $\lambda \in (0,\Lambda )$ , one positive solution for $\lambda =\Lambda $ , and no positive solution for $\lambda >\Lambda
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Longtime dynamics of solutions for higher-order \((m_{1},m_{2})\)-coupled Kirchhoff models with higher-order rotational inertia and nonlocal damping Bound. Value Probl. (IF 1.7) Pub Date : 2024-04-04 Penghui Lv, Yuan Yuan, Guoguang Lin
The Kirchhoff model is derived from the vibration problem of stretchable strings. This paper focuses on the longtime dynamics of a higher-order $(m_{1},m_{2})$ -coupled Kirchhoff system with higher-order rotational inertia and nonlocal damping. We first obtain the state of the model’s solutions in different spaces through prior estimation. After that, we immediately prove the existence and uniqueness
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Asymptotic behaviour and boundedness of solutions for third-order stochastic differential equation with multi-delay Bound. Value Probl. (IF 1.7) Pub Date : 2024-04-02 A. M. Mahmoud, D. A. Eisa, R. O. A. Taie, D. A. M. Bakhit
In the present paper, we study stochastic stability and stochastic boundedness for the stochastic differential equation (SDE) with multi-delay of third order. The derived results extend and improve some earlier results in the relevant literature, which are related to the qualitative properties of solutions to third-order delay differential equations (DDEs) and SDEs with multi-delay. Two examples are
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Application of double Sumudu-generalized Laplace decomposition method and two-dimensional time-fractional coupled Burger’s equation Bound. Value Probl. (IF 1.7) Pub Date : 2024-03-29 Hassan Eltayeb
The current paper concentrates on discovering the exact solutions of the time-fractional regular and singular coupled Burger’s equations by involving a new technique known as the double Sumudu-generalized Laplace and Adomian decomposition method. Furthermore, some theorems of the double Sumudu-generalized Laplace properties are proved. Further, the offered method is a powerful tool for solving an enormous
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A novel stability analysis of functional equation in neutrosophic normed spaces Bound. Value Probl. (IF 1.7) Pub Date : 2024-03-29 Ahmad Aloqaily, P. Agilan, K. Julietraja, S. Annadurai, Nabil Mlaiki
The analysis of stability in functional equations (FEs) within neutrosophic normed spaces is a significant challenge due to the inherent uncertainties and complexities involved. This paper proposes a novel approach to address this challenge, offering a comprehensive framework for investigating stability properties in such contexts. Neutrosophic normed spaces are a generalization of traditional normed
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Solvability of a nonlinear second order m-point boundary value problem with p-Laplacian at resonance Bound. Value Probl. (IF 1.7) Pub Date : 2024-03-29 Meiyu Liu, Minghe Pei, Libo Wang
We study the existence of solutions of the nonlinear second order m-point boundary value problem with p-Laplacian at resonance $$ \textstyle\begin{cases} (\phi _{p}(x'))'=f(t,x,x'),\quad t\in [0,1],\\ x'(0)=0, \qquad x(1)=\sum_{i=1}^{m-2}a_{i}x(\xi _{i}), \end{cases} $$ where $\phi _{p}(s)=|s|^{p-2}s$ , $p>1$ , $f:[0,1]\times \mathbb{R}^{2}\to \mathbb{R}$ is a continuous function, $a_{i}>0$ ( $i=1
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Infinitely many solutions for three quasilinear Laplacian systems on weighted graphs Bound. Value Probl. (IF 1.7) Pub Date : 2024-03-28 Yan Pang, Junping Xie, Xingyong Zhang
We investigate a generalized poly-Laplacian system with a parameter on weighted finite graphs, a generalized poly-Laplacian system with a parameter and Dirichlet boundary value on weighted locally finite graphs, and a $(p,q)$ -Laplacian system with a parameter on weighted locally finite graphs. We utilize a critical points theorem built by Bonanno and Bisci [Bonanno, Bisci, and Regan, Math. Comput
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On a new version of Hermite–Hadamard-type inequality based on proportional Caputo-hybrid operator Bound. Value Probl. (IF 1.7) Pub Date : 2024-03-28 Tuba Tunç, İzzettin Demir
In mathematics and the applied sciences, as a very useful tool, fractional calculus is a basic concept. Furthermore, in many areas of mathematics, it is better to use a new hybrid fractional operator, which combines the proportional and Caputo operators. So we concentrate on the proportional Caputo-hybrid operator because of its numerous applications. In this research, we introduce a novel extension
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Mixed boundary value problems involving Sturm–Liouville differential equations with possibly negative coefficients Bound. Value Probl. (IF 1.7) Pub Date : 2024-03-28 Gabriele Bonanno, Giuseppina D’Aguì, Valeria Morabito
This paper is devoted to the study of a mixed boundary value problem for a complete Sturm–Liouville equation, where the coefficients can also be negative. In particular, the existence of infinitely many distinct positive solutions to the given problem is obtained by using critical point theory.
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Singular perturbation boundary and interior layers problems with multiple turning points Bound. Value Probl. (IF 1.7) Pub Date : 2024-03-28 Xinyu Wang, Na Wang
In the study of singularly perturbed boundary problems with turning points, the solution undergoes sharp changes near these points and exhibits various interior phenomena. We employ the matching asymptotic expansion method to analyze and solve a singularly perturbed boundary and interior layers problem with multiple turning points, resulting in a composite expansion that fits well with the numerical
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Positive solutions for the Riemann–Liouville-type fractional differential equation system with infinite-point boundary conditions on infinite intervals Bound. Value Probl. (IF 1.7) Pub Date : 2024-03-27 Yang Yu, Qi Ge
In this paper, we study the existence and uniqueness of positive solutions for a class of a fractional differential equation system of Riemann–Liouville type on infinite intervals with infinite-point boundary conditions. First, the higher-order equation is reduced to the lower-order equation, and then it is transformed into the equivalent integral equation. Secondly, we obtain the existence and uniqueness
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Gradient estimates for a class of elliptic equations with logarithmic terms Bound. Value Probl. (IF 1.7) Pub Date : 2024-03-25 Ze Gao, Qiming Guo
We obtain the gradient estimates of the positive solutions to a nonlinear elliptic equation on an n-dimensional complete Riemannian manifold $(M, g)$ $$ \Delta u +au(\ln{u})^{p}+bu\ln{u}=0, $$ where $a\ne 0$ , b are two constants and $p=\frac{k_{1}}{2k_{2}+1}\ge 2$ , here $k_{1}$ and $k_{2}$ are two positive integers. The gradient bound is independent of the bounds of the solution and the Laplacian
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Competing anisotropic and Finsler \((p,q)\)-Laplacian problems Bound. Value Probl. (IF 1.7) Pub Date : 2024-03-25 Dumitru Motreanu, Abdolrahman Razani
The aim of this paper is to prove the existence of generalized variational solutions for nonlinear Dirichlet problems driven by anisotropic and Finsler Laplacian competing operators. The main difficulty consists in the lack of ellipticity and monotonicity in the principal part of the equations. This difficulty is overcome by developing a Galerkin-type procedure.
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A hybrid method to solve a fractional-order Newell–Whitehead–Segel equation Bound. Value Probl. (IF 1.7) Pub Date : 2024-03-18 Umut Bektaş, Halil Anaç
This paper solves fractional differential equations using the Shehu transform in combination with the q-homotopy analysis transform method (q-HATM). As the Shehu transform is only applicable to linear equations, q-HATM is an efficient technique for approximating solutions to nonlinear differential equations. In nonlinear systems that explain the emergence of stripes in 2D systems, the Newell–Whitehead–Segel
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Existence and multiplicity of solutions for fractional \(p_{1}(x,\cdot )\& p_{2}(x,\cdot )\)-Laplacian Schrödinger-type equations with Robin boundary conditions Bound. Value Probl. (IF 1.7) Pub Date : 2024-03-13 Zhenfeng Zhang, Tianqing An, Weichun Bu, Shuai Li
In this paper, we study fractional $p_{1}(x,\cdot )\& p_{2}(x,\cdot )$ -Laplacian Schrödinger-type equations for Robin boundary conditions. Under some suitable assumptions, we show that two solutions exist using the mountain pass lemma and Ekeland’s variational principle. Then, the existence of infinitely many solutions is derived by applying the fountain theorem and the Krasnoselskii genus theory
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Blow-up and lifespan of solutions for elastic membrane equation with distributed delay and logarithmic nonlinearity Bound. Value Probl. (IF 1.7) Pub Date : 2024-03-08 Salah Boulaaras, Rashid Jan, Abdelbaki Choucha, Aderrahmane Zaraï, Mourad Benzahi
We examine a Kirchhoff-type equation with nonlinear viscoelastic properties, characterized by distributed delay, logarithmic nonlinearity, and Balakrishnan–Taylor damping terms (elastic membrane equation). Under appropriate hypotheses, we establish the occurrence of solution blow-up.
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Caputo fractional backward stochastic differential equations driven by fractional Brownian motion with delayed generator Bound. Value Probl. (IF 1.7) Pub Date : 2024-03-07 Yunze Shao, Junjie Du, Xiaofei Li, Yuru Tan, Jia Song
Over the years, the research of backward stochastic differential equations (BSDEs) has come a long way. As a extension of the BSDEs, the BSDEs with time delay have played a major role in the stochastic optimal control, financial risk, insurance management, pricing, and hedging. In this paper, we study a class of BSDEs with time-delay generators driven by Caputo fractional derivatives. In contrast to
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Positive solutions for a semipositone anisotropic p-Laplacian problem Bound. Value Probl. (IF 1.7) Pub Date : 2024-03-01 A. Razani, Giovany M. Figueiredo
In this paper, a semipositone anisotropic p-Laplacian problem $$ -\Delta _{\overrightarrow{p}}u=\lambda f(u), $$ on a bounded domain with the Dirchlet boundary condition is considered, where $A(u^{q}-1)\leq f(u)\leq B(u^{q}-1)$ for $u>0$ , $f(0)<0$ and $f(u)=0$ for $u\leq -1$ . It is proved that there exists $\lambda ^{*}>0$ such that if $\lambda \in (0,\lambda ^{*})$ , then the problem has a positive
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Optimal decay-in-time rates of solutions to the Cauchy problem of 3D compressible magneto-micropolar fluids Bound. Value Probl. (IF 1.7) Pub Date : 2024-02-29 Xinyu Cui, Shengbin Fu, Rui Sun, Fangfang Tian
This paper focuses on the long time behavior of the solutions to the Cauchy problem of the three-dimensional compressible magneto-micropolar fluids. More precisely, we aim to establish the optimal rates of temporal decay for the highest-order spatial derivatives of the global strong solutions by the method of decomposing frequency. Our result can be regarded as the further investigation of the one
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Generalized strongly n-polynomial convex functions and related inequalities Bound. Value Probl. (IF 1.7) Pub Date : 2024-02-26 Serap Özcan, Mahir Kadakal, İmdat İşcan, Huriye Kadakal
This paper focuses on introducing and examining the class of generalized strongly n-polynomial convex functions. Relationships between these functions and other types of convex functions are explored. The Hermite–Hadamard inequality is established for generalized strongly n-polynomial convex functions. Additionally, new integral inequalities of Hermite–Hadamard type are derived for this class of functions
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Quasilinear Schrödinger equations with superlinear terms describing the Heisenberg ferromagnetic spin chain Bound. Value Probl. (IF 1.7) Pub Date : 2024-02-23 Yongkuan Cheng, Yaotian Shen
In this paper, we consider a model problem arising from a classical planar Heisenberg ferromagnetic spin chain: $$ -\Delta u+V(x)u-\frac{u}{\sqrt{1-u^{2}}}\Delta \sqrt{1-u^{2}}=c \vert u \vert ^{p-2}u,\quad x\in \mathbb{R}^{N}, $$ where $2< p<2^{*}$ , $c>0$ and $N\geq 3$ . By the cutoff technique, the change of variables and the $L^{\infty}$ estimate, we prove that there exists $c_{0}>0$ , such that
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Upper and lower solutions method for a class of second-order coupled systems Bound. Value Probl. (IF 1.7) Pub Date : 2024-02-23 Zelong Yu, Zhanbing Bai, Suiming Shang
This paper provides a class of upper and lower solution definitions for second-order coupled systems by transforming the fourth-order differential equation into a second-order differential system. Then, by constructing a homotopy parameter and utilizing the maximum principle, we propose an upper and lower solutions method for studying a class of second-order coupled systems with Dirichlet boundary
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The Robin problems for the coupled system of reaction–diffusion equations Bound. Value Probl. (IF 1.7) Pub Date : 2024-02-23 Po-Chun Huang, Bo-Yu Pan
This article investigates the local well-posedness of Turing-type reaction–diffusion equations with Robin boundary conditions in the Sobolev space. Utilizing the Hadamard norm, we derive estimates for Fokas unified transform solutions for linear initial-boundary value problems subject to external forces. Subsequently, we demonstrate that the iteration map, defined by the unified transform solutions
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Existence and stability of a q-Caputo fractional jerk differential equation having anti-periodic boundary conditions Bound. Value Probl. (IF 1.7) Pub Date : 2024-02-22 Khansa Hina Khalid, Akbar Zada, Ioan-Lucian Popa, Mohammad Esmael Samei
In this work, we analyze a q-fractional jerk problem having anti-periodic boundary conditions. The focus is on investigating whether a unique solution exists and remains stable under specific conditions. To prove the uniqueness of the solution, we employ a Banach fixed point theorem and a mathematical tool for establishing the presence of distinct fixed points. To demonstrate the availability of a
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Hybrid cubic and hyperbolic b-spline collocation methods for solving fractional Painlevé and Bagley-Torvik equations in the Conformable, Caputo and Caputo-Fabrizio fractional derivatives Bound. Value Probl. (IF 1.7) Pub Date : 2024-02-20 Nahid Barzehkar, Reza Jalilian, Ali Barati
In this paper, we approximate the solution of fractional Painlevé and Bagley-Torvik equations in the Conformable (Co), Caputo (C), and Caputo-Fabrizio (CF) fractional derivatives using hybrid hyperbolic and cubic B-spline collocation methods, which is an extension of the third-degree B-spline function with more smoothness. The hybrid B-spline function is flexible and produces a system of band matrices
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Existence and multiplicity of solutions of fractional differential equations on infinite intervals Bound. Value Probl. (IF 1.7) Pub Date : 2024-02-08 Weichen Zhou, Zhaocai Hao, Martin Bohner
In this research, we investigate the existence and multiplicity of solutions for fractional differential equations on infinite intervals. By using monotone iteration, we identify two solutions, and the multiplicity of solutions is demonstrated by the Leggett–Williams fixed point theorem.
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Existence of normalized solutions for Schrödinger systems with linear and nonlinear couplings Bound. Value Probl. (IF 1.7) Pub Date : 2024-02-08 Zhaoyang Yun, Zhitao Zhang
In this paper we study the nonlinear Bose–Einstein condensates Schrödinger system $$ \textstyle\begin{cases} -\Delta u_{1}-\lambda _{1} u_{1}=\mu _{1} u_{1}^{3}+\beta u_{1}u_{2}^{2}+ \kappa (x) u_{2}\quad\text{in }\mathbb{R}^{3}, \\ -\Delta u_{2}-\lambda _{2} u_{2}=\mu _{2} u_{2}^{3}+\beta u_{1}^{2}u_{2}+ \kappa (x) u_{1}\quad\text{in }\mathbb{R}^{3}, \\ \int _{\mathbb{R}^{3}} u_{1}^{2}=a_{1}^{2},\qquad
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Infinitely many solutions for quasilinear Schrödinger equation with concave-convex nonlinearities Bound. Value Probl. (IF 1.7) Pub Date : 2024-02-06 Lijuan Chen, Caisheng Chen, Qiang Chen, Yunfeng Wei
In this work, we study the existence of infinitely many solutions to the following quasilinear Schrödinger equations with a parameter α and a concave-convex nonlinearity: 0.1 $$\begin{aligned}& -\Delta _{p}u+V(x) \vert u \vert ^{p-2}u-\Delta _{p}\bigl( \vert u \vert ^{2\alpha}\bigr) \vert u \vert ^{2\alpha -2}u= \lambda h_{1}(x) \vert u \vert ^{m-2}u+h_{2}(x) \vert u \vert ^{q-2}u, \\& \quad x\in {\mathbb{R}}^{N}
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Infinite system of nonlinear tempered fractional order BVPs in tempered sequence spaces Bound. Value Probl. (IF 1.7) Pub Date : 2024-02-01 Sabbavarapu Nageswara Rao, Mahammad Khuddush, Ahmed Hussein Msmali, Abdullah Ali H. Ahmadini
This paper deals with the existence results of the infinite system of tempered fractional BVPs $$\begin{aligned}& {}^{\mathtt{R}}_{0}\mathrm{D}_{\mathrm{r}}^{\varrho , \uplambda} \mathtt{z}_{\mathtt{j}}(\mathrm{r})+\psi _{\mathtt{j}}\bigl(\mathrm{r}, \mathtt{z}(\mathrm{r})\bigr)=0,\quad 0< \mathrm{r}< 1, \\& \mathtt{z}_{\mathtt{j}}(0)=0,\qquad {}^{\mathtt{R}}_{0} \mathrm{D}_{ \mathrm{r}}^{\mathtt{m}
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Nonexistence of positive solutions for the weighted higher-order elliptic system with Navier boundary condition Bound. Value Probl. (IF 1.7) Pub Date : 2024-01-26 Weiwei Zhao, Xiaoling Shao, Changhui Hu, Zhiyu Cheng
We establish a Liouville-type theorem for a weighted higher-order elliptic system in a wider exponent region described via a critical curve. We first establish a Liouville-type theorem to the involved integral system and then prove the equivalence between the two systems by using superharmonic properties of the differential systems. This improves the results in (Complex Var. Elliptic Equ. 5:1436–1450
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Blow-up solutions for a 4-dimensional semilinear elliptic system of Liouville type in some general cases Bound. Value Probl. (IF 1.7) Pub Date : 2024-01-25 Sami Baraket, Anis Ben Ghorbal, Rima Chetouane, Azedine Grine
This paper is devoted to the existence of singular limit solutions for a nonlinear elliptic system of Liouville type under Navier boundary conditions in a bounded open domain of $\mathbb{R}^{4}$ . The concerned results are obtained employing the nonlinear domain decomposition method and a Pohozaev-type identity.
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Least energy nodal solutions for a weighted \((N, p)\)-Schrödinger problem involving a continuous potential under exponential growth nonlinearity Bound. Value Probl. (IF 1.7) Pub Date : 2024-01-25 Sami Baraket, Brahim Dridi, Azedine Grine, Rached Jaidane
This article aims to investigate the existence of nontrivial solutions with minimal energy for a logarithmic weighted $(N,p)$ -Laplacian problem in the unit ball B of $\mathbb{R}^{N}$ , $N>2$ . The nonlinearities of the equation are critical or subcritical growth, which is motivated by weighted Trudinger–Moser type inequalities. Our approach is based on constrained minimization within the Nehari set
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New type of the unique continuation property for a fractional diffusion equation and an inverse source problem Bound. Value Probl. (IF 1.7) Pub Date : 2024-01-23 Wenyi Liu, Chengbin Du, Zhiyuan Li
In this work, a new type of the unique continuation property for time-fractional diffusion equations is studied. The proof is mainly based on the Laplace transform and the properties of Bessel functions. As an application, the uniqueness of the inverse problem in the simultaneous determination of spatially dependent source terms and fractional order from sparse boundary observation data is established
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A necessary and sufficient condition for the existence of global solutions to reaction-diffusion equations on bounded domains Bound. Value Probl. (IF 1.7) Pub Date : 2024-01-22 Soon-Yeong Chung, Jaeho Hwang
The purpose of this paper is to give a necessary and sufficient condition for the existence and non-existence of global solutions of the following semilinear parabolic equations $$ u_{t}=\Delta u+\psi (t)f(u),\quad \text{in }\Omega \times (0,\infty ), $$ under the mixed boundary condition on a bounded domain Ω. In fact, this has remained an open problem for a few decades, even for the case $f(u)=u^{p}$
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Existence and optimal controls of non-autonomous for impulsive evolution equation without Lipschitz assumption Bound. Value Probl. (IF 1.7) Pub Date : 2024-01-19 Lixin Sheng, Weimin Hu, You-Hui Su
In this paper, we investigate the existence of mild solutions as well as optimal controls for non-autonomous impulsive evolution equations with nonlocal conditions. Using the Schauder’s fixed-point theorem as well as the theory of evolution family, we prove the existence of mild solutions for the concerned problem. Furthermore, without the Lipschitz continuity of the nonlinear term, the optimal control
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On a composite obtained by a mixture of a dipolar solid with a Moore–Gibson–Thompson media Bound. Value Probl. (IF 1.7) Pub Date : 2024-01-19 Marin Marin, Sorin Vlase, Denisa Neagu
Our study is dedicated to a mixture composed of a dipolar elastic medium and a viscous Moore–Gibson–Thompson (MGT) material. The mixed problem with initial and boundary data, considered in this context, is approached from the perspective of the existence of a solution to this problem as well as the uniqueness of the solution. Considering that the mixed problem is very complex, both from the point of
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Bifurcations, chaotic behavior, sensitivity analysis, and various soliton solutions for the extended nonlinear Schrödinger equation Bound. Value Probl. (IF 1.7) Pub Date : 2024-01-19 Mati ur Rahman, Mei Sun, Salah Boulaaras, Dumitru Baleanu
In this manuscript, our primary objective is to delve into the intricacies of an extended nonlinear Schrödinger equation. To achieve this, we commence by deriving a dynamical system tightly linked to the equation through the Galilean transformation. We then employ principles from planar dynamical systems theory to explore the bifurcation phenomena exhibited within this derived system. To investigate
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Three solutions for fractional elliptic systems involving ψ-Hilfer operator Bound. Value Probl. (IF 1.7) Pub Date : 2024-01-18 Rafik Guefaifia, Tahar Bouali, Salah Boulaaras
In this paper, using variational methods introduced in the previous study on fractional elliptic systems, we prove the existence of at least three weak solutions for an elliptic nonlinear system with a p-Laplacian ψ-Hilfer operator.
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A fixed point result on an extended neutrosophic rectangular metric space with application Bound. Value Probl. (IF 1.7) Pub Date : 2024-01-18 Gunaseelan Mani, Maria A. R. M. Antony, Zoran D. Mitrović, Ahmad Aloqaily, Nabil Mlaiki
In this paper, we propose the notion of extended neutrosophic rectangular metric space and prove some fixed point results under contraction mapping. Finally, as an application of the obtained results, we prove the existence and uniqueness of the Caputo fractional differential equation.
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Novel results of Milne-type inequalities involving tempered fractional integrals Bound. Value Probl. (IF 1.7) Pub Date : 2024-01-18 Fatih Hezenci, Hüseyin Budak, Hasan Kara, Umut Baş
In this current research, we focus on the domain of tempered fractional integrals, establishing a novel identity that serves as the cornerstone of our study. This identity paves the way for the Milne-type inequalities, which are explored through the framework of differentiable convex mappings inclusive of tempered fractional integrals. The significance of these mappings in the realm of fractional calculus
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Dynamical behavior of a degenerate parabolic equation with memory on the whole space Bound. Value Probl. (IF 1.7) Pub Date : 2024-01-17 Rong Guo, Xuan Leng
This paper is concerned with the existence and uniqueness of global attractors for a class of degenerate parabolic equations with memory on $\mathbb{R}^{n}$ . Since the corresponding equation includes the degenerate term $\operatorname{div}\{a(x)\nabla u\}$ , it requires us to give appropriate assumptions about the weight function $a(x)$ for studying our problem. Based on this, we first obtain the
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Spectral element discretization of the time-dependent Stokes problem with nonstandard boundary conditions Bound. Value Probl. (IF 1.7) Pub Date : 2024-01-10 Mohamed Abdelwahed, Nejmeddine Chorfi
This work deals with the spectral element discretization of the time-dependent Stokes problem in two- and three-dimensional domains. The boundary condition is defined on the normal component of the velocity and the tangential components of the vorticity. The discretization related to the time variable is processed by a Backward Euler method. We prove through a detailed numerical analysis the well-posedness
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Continuity and pullback attractors for a semilinear heat equation on time-varying domains Bound. Value Probl. (IF 1.7) Pub Date : 2024-01-08 Mingli Hong, Feng Zhou, Chunyou Sun
We consider dynamics of a semilinear heat equation on time-varying domains with lower regular forcing term. Instead of requiring the forcing term $f(\cdot )$ to satisfy $\int _{-\infty}^{t}e^{\lambda s}\|f(s)\|^{2}_{L^{2}}\,ds<\infty $ for all $t\in \mathbb{R}$ , we show that the solutions of a semilinear heat equation on time-varying domains are continuous with respect to initial data in $H^{1}$ topology
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Sign-changing solutions for Kirchhoff-type variable-order fractional Laplacian problems Bound. Value Probl. (IF 1.7) Pub Date : 2024-01-05 Jianwen Zhou, Yueting Yang, Wenbo Wang
In this paper, we are concerned with the Kirchhoff-type variable-order fractional Laplacian problems involving critical exponents and logarithmic nonlinearity. By using the constraint variational method, we show the existence of one least energy sign-changing solution. Moreover, we show that this energy is strictly larger than twice the ground energy.
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Time decay of solutions for compressible isentropic non-Newtonian fluids Bound. Value Probl. (IF 1.7) Pub Date : 2024-01-03 Jialiang Wang, Han Jiang
In this paper, we consider the Cauchy problem of a compressible Navier–Stokes system of Eills-type non-Newtonian fluids. We investigate the time decay properties of classical solutions for the compressible non-Newtonian fluid equations. More specifically, we construct a new linearized system in terms of a combination of the solutions, and then we investigate the long-time behavior of the Cauchy problem
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Ground-state sign-changing homoclinic solutions for a discrete nonlinear p-Laplacian equation with logarithmic nonlinearity Bound. Value Probl. (IF 1.7) Pub Date : 2024-01-02 Xin Ou, Xingyong Zhang
By using a direct non-Nehari manifold method from (Tang and Cheng in J. Differ. Equ. 261:2384–2402, 2016), we obtain an existence result of ground-state sign-changing homoclinic solutions that only changes sign once and ground-state homoclinic solutions for a class of discrete nonlinear p-Laplacian equations with logarithmic nonlinearity. Moreover, we prove that the sign-changing ground-state energy
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Existence and uniqueness of solutions for multi-order fractional differential equations with integral boundary conditions Bound. Value Probl. (IF 1.7) Pub Date : 2024-01-02 Jian-Ping Sun, Li Fang, Ya-Hong Zhao, Qian Ding
In this paper, we consider the existence and uniqueness of solutions for the following nonlinear multi-order fractional differential equation with integral boundary conditions $$ \textstyle\begin{cases} ({}^{C}D_{0+}^{\alpha}u)(t)+\sum_{i=1}^{m}\lambda _{i}(t)({}^{C}D_{0+}^{\alpha _{i}}u)(t)+ \sum_{j=1}^{n}\mu _{j}(t)({}^{C}D_{0+}^{\beta _{j}}u)(t)\\ \quad{}+\sum_{k=1}^{p}\xi _{k}(t)({}^{C}D_{0+}^{\gamma
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Nodal solutions for Neumann systems with gradient dependence Bound. Value Probl. (IF 1.7) Pub Date : 2024-01-02 Kamel Saoudi, Eadah Alzahrani, Dušan D. Repovš
We consider the following convective Neumann systems: $$ ( \mathrm{S} ) \quad \textstyle\begin{cases} -\Delta _{p_{1}}u_{1}+ \frac{ \vert \nabla u_{1} \vert ^{p_{1}}}{u_{1}+\delta _{1} }=f_{1}(x,u_{1},u_{2}, \nabla u_{1},\nabla u_{2}) & \text{in } \Omega , \\ -\Delta _{p_{2}}u_{2}+ \frac{ \vert \nabla u_{2} \vert ^{p_{2}}}{u_{2}+\delta _{2} }=f_{2}(x,u_{1},u_{2}, \nabla u_{1},\nabla u_{2}) & \text{in
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Periodic solutions for second-order even and noneven Hamiltonian systems Bound. Value Probl. (IF 1.7) Pub Date : 2024-01-02 Juan Xiao, Xueting Chen
In this paper, we consider the second-order Hamiltonian system $$ \ddot{x}+V^{\prime}(x)=0,\quad x\in \mathbb{R}^{N}. $$ We use the monotonicity assumption introduced by Bartsch and Mederski (Arch. Ration. Mech. Anal. 215:283–306, 2015). When V is even, we can release the strict convexity hypothesis, which is used by Bartsch and Mederski combined with the monotonicity assumption. When V is noneven
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Ground state solutions for a kind of superlinear elliptic equations with variable exponent Bound. Value Probl. (IF 1.7) Pub Date : 2024-01-02 Bosheng Xiao, Qiongfen Zhang
In this paper, we focus on the existence of ground state solutions for the $p(x)$ -Laplacian equation $$ \textstyle\begin{cases} -\Delta _{p(x)}u+\lambda \vert u \vert ^{p(x)-2}u=f(x,u)+h(x) \quad \text{in } \Omega , \\ u=0,\quad \text{on }\partial \Omega . \end{cases} $$ Using the constraint variational method, quantitative deformation lemma, and strong maximum principle, we proved that the above
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Extinction behavior and recurrence of n-type Markov branching–immigration processes Bound. Value Probl. (IF 1.7) Pub Date : 2024-01-02 Junping Li, Juan Wang
In this paper, we consider n-type Markov branching–immigration processes. The uniqueness criterion is first established. Then, we construct a related system of differential equations based on the branching property. Furthermore, the explicit expression of extinction probability and the mean extinction time are successfully obtained in the absorbing case by using the unique solution of the related system
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Periodic dynamics of predator-prey system with Beddington–DeAngelis functional response and discontinuous harvesting Bound. Value Probl. (IF 1.7) Pub Date : 2023-12-15 Yingying Wang, Zhinan Xia
This paper investigates a delayed predator-prey model with discontinuous harvesting and Beddington–DeAngelis functional response. Using the theory of differential inclusion theory, the existence of positive solutions in the sense of Filippov is discussed. Under reasonable assumptions and periodic disturbances, the existence of positive periodic solutions of the model is studied based on the theory
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Hybrid interpolative mappings for solving fractional Navier–Stokes and functional differential equations Bound. Value Probl. (IF 1.7) Pub Date : 2023-12-14 Hasanen A. Hammad, Hassen Aydi, Doha A. Kattan
The purpose of this study is to establish fixed-point results for new interpolative contraction mappings in the setting of Busemann space involving a convex hull. To illustrate our findings, we also offer helpful and compelling examples. Finally, the theoretical results are applied to study the existence of solutions to fractional Navier–Stokes and fractional-functional differential equations as applications
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Existence theory and Ulam’s stabilities for switched coupled system of implicit impulsive fractional order Langevin equations Bound. Value Probl. (IF 1.7) Pub Date : 2023-12-12 Rizwan Rizwan, Fengxia Liu, Zhiyong Zheng, Choonkil Park, Siriluk Paokanta
In this work, a system of nonlinear, switched, coupled, implicit, impulsive Langevin equations with two Hilfer fractional derivatives is introduced. The suitable conditions and results are established to discuss existence, uniqueness, and Ulam-type stability results of the mentioned model, with the help of nonlinear functional analysis techniques and Banach’s fixed-point theorem. Furthermore, we examine
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Existence and multiplicity of solutions for boundary value problem of singular two-term fractional differential equation with delay and sign-changing nonlinearity Bound. Value Probl. (IF 1.7) Pub Date : 2023-12-08 Rulan Bai, Kemei Zhang, Xue-Jun Xie
In this paper, we consider the existence of solutions for a boundary value problem of singular two-term fractional differential equation with delay and sign-changing nonlinearity. By means of the Guo–Krasnosel’skii fixed point theorem and the Leray–Schauder nonlinear alternative theorem, we obtain some results on the existence and multiplicity of solutions, respectively.
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Boundary value problems of quaternion-valued differential equations: solvability and Green’s function Bound. Value Probl. (IF 1.7) Pub Date : 2023-11-27 Jie Liu, Siyu Sun, Zhibo Cheng
This paper is associated with Sturm–Liouville type boundary value problems and periodic boundary value problems for quaternion-valued differential equations (QDEs). Employing the theory of quaternionic matrices, we prove the conditions for the solvability of the linear boundary valued problem and find Green’s function.