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Single peak solutions for an elliptic system of FitzHugh–Nagumo type J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2024-03-27 Bingqi Wang, Xiangyu Zhou
We study the Dirichlet problem for an elliptic system derived from FitzHugh–Nagummo model as follows: $$\begin{aligned} \left\{ \begin{aligned}&-\varepsilon ^2\Delta u =f(u)- v, \qquad&\text {in}\ \Omega ,\\&-\Delta v+\gamma v =\delta _\varepsilon u,&\text{ in }\ \Omega ,\\&u=v =0,&\text {on}\ \partial \Omega , \end{aligned} \right. \end{aligned}$$ where \(\Omega \) represents a bounded smooth domain
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Functional determinants for the second variation J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2024-03-23 Stefano Baranzini
We study the determinant of the second variation of an optimal control problem for general boundary conditions. Generically, these operators are not trace class and the determinant is defined as a principal value limit. We provide a formula to compute this determinant in terms of the linearisation of the extrenal flow. We illustrate the procedure in some special cases, proving some Hill-type formulas
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Positive solution for an elliptic system with critical exponent and logarithmic terms: the higher-dimensional cases J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2024-03-18
Abstract In this paper, we consider the coupled elliptic system with critical exponent and logarithmic terms: $$\begin{aligned} {\left\{ \begin{array}{ll} -\Delta u=\lambda _{1}u+ \mu _1|u|^{2p-2}u+\beta |u|^{p-2}|v|^{p}u+\theta _1 u\log u^2, &{} \quad x\in \Omega ,\\ -\Delta v=\lambda _{2}v+ \mu _2|v|^{2p-2}v+\beta |u|^{p}|v|^{p-2}v+\theta _2 v\log v^2, &{}\quad x\in \Omega ,\\ u=v=0, &{}\quad x \in
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Existence results for singular strongly non-linear integro-differential BVPs on the half line J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2024-03-17 Francesca Anceschi
This work is devoted to the study of singular strongly non-linear integro-differential equations of the type $$\begin{aligned} (\Phi (k(t)v'(t)))'=f\left( t,\int _0^t v(s)\, \textrm{d}s,v(t),v'(t) \right) , \text{ a.e. } \text{ on } {\mathbb {R}}^{+}_0 := [0, + \infty [, \end{aligned}$$ where f is a Carathéodory function, \(\Phi \) is a strictly increasing homeomorphism, and k is a non-negative integrable
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Existence and multiplicity of solutions of Stieltjes differential equations via topological methods J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2024-02-23 Věra Krajščáková, F. Adrián F. Tojo
In this work, we use techniques from Stieltjes calculus and fixed point index theory to show the existence and multiplicity of solution of a first order non-linear boundary value problem with linear boundary conditions that extend the periodic case. We also provide the Green’s function associated to the problem as well as an example of application.
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Stability of the braid types defined by the symplecticmorphisms preserving a link J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2024-02-13
Abstract Fix a suitable link on the disk. Recently, F. Morabito associates each Hamiltonian symplecticmorphism preserving the link to a braid type. Based on this construction, Morabito defines a family of pseudometrics on the braid groups by using the Hofer metric. In this paper, we show that two Hamiltonian symplecticmorphisms define the same braid type provided that their Hofer distance is sufficiently
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Multiple ordered solutions for a class of quasilinear problem with oscillating nonlinearity J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2024-02-13 Gelson C. G. dos Santos, Julio Roberto S. Silva
In this paper, we use truncation argument combined with method of minimization, argument of comparison, topological degree arguments and sub-supersolutions method to show existence of multiple positive solutions (which are ordered in the \(C(\overline{\Omega })\)-norm) for the following class of problems: $$\begin{aligned} \left\{ \begin{aligned} -&\Delta u - \kappa \Delta (u^{2}) u +\mu |u|^{q-2}u
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Vũ Ngọc’s conjecture on focus-focus singular fibers with multiple pinched points J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2024-01-25 Álvaro Pelayo, Xiudi Tang
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Simple closed geodesics in dimensions $$\ge 3$$ J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2024-01-19
Abstract We show that for a generic Riemannian or reversible Finsler metric on a compact differentiable manifold M of dimension at least three all closed geodesics are simple and do not intersect each other. Using results by Contreras (Ann Math 2(172):761–808, 2010; in: Proceedings of International Congress Mathematicians (ICM 2010) Hyderabad, India, pp 1729–1739, 2011) this shows that for a generic
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Transverse foliations in the rotating Kepler problem J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2024-01-19 Seongchan Kim
We construct finite energy foliations and transverse foliations of neighbourhoods of the circular orbits in the rotating Kepler problem for all negative energies. This paper would be a first step towards our ultimate goal that is to recover and refine McGehee’s results on homoclinics [23] and to establish a theoretical foundation to the numerical demonstration of the existence of a homoclinic–heteroclinic
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Cuplength estimates for time-periodic measures of Hamiltonian systems with diffusion J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2024-01-10 Oliver Fabert
We show how methods from Hamiltonian Floer theory can be used to establish lower bounds for the number of different time-periodic measures of time-periodic Hamiltonian systems with diffusion. After proving the existence of closed random periodic solutions and of the corresponding Floer curves for Hamiltonian systems with random walks with step width 1/n for every \(n\in \mathbb {N}\), we show that
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Existence of non-radial solutions to semilinear elliptic systems on a unit ball in $${\mathbb {R}}^3$$ J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2023-11-20 Jingzhou Liu, Carlos García-Azpeitia, Wieslaw Krawcewicz
In this paper, we prove the existence of non-radial solutions to the problem \(-\triangle u= f(x,u)\), \(u|_{\partial \Omega }=0\) on the unit ball \(\Omega :=\{x\in {\mathbb {R}}^3: \Vert x\Vert <1\}\) with \(u(x)\in {\mathbb {R}}^s\), where f is a sub-linear continuous function, differentiable with respect to u at zero and satisfying \(f(gx,u) = f(x,u)\) for all \(g\in O(3)\), \( f(x,-u)=- f(x,u)\)
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Slicing the Nash equilibrium manifold J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2023-11-13 Yehuda John Levy
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Nielsen numbers of affine n-valued maps on nilmanifolds J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2023-10-25 C. Deconinck, K. Dekimpe
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Elliptic problems with mixed nonlinearities and potentials singular at the origin and at the boundary of the domain J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2023-10-16 Bartosz Bieganowski, Adam Konysz
We are interested in the following Dirichlet problem: $$\begin{aligned} \left\{ \begin{array}{ll} -\Delta u + \lambda u - \mu \frac{u}{|x|^2} - \nu \frac{u}{\textrm{dist}(x,\mathbb {R}^N \setminus \Omega )^2} = f(x,u) &{} \quad \text{ in } \Omega \\ u = 0 &{} \quad \text{ on } \partial \Omega , \end{array} \right. \end{aligned}$$ on a bounded domain \(\Omega \subset \mathbb {R}^N\) with \(0 \in \Omega
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On a biharmonic elliptic problem with slightly subcritical non-power nonlinearity J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2023-10-13 Shengbing Deng, Fang Yu
We study the following biharmonic elliptic problem with slightly subcritical non-power nonlinearity: $$\begin{aligned} \left\{ \begin{array}{lll} \Delta ^2 u =\frac{|u|^{2^*-2}u}{[\ln (e+|u|)]^\varepsilon }\ \ &{}\textrm{in}\ \Omega , \\ u=\Delta u= 0 \ \ &{} \textrm{on}\ \partial \Omega , \end{array} \right. \end{aligned}$$ where \(2^*=\frac{2n}{n-4}\), \(\Omega \) is a bounded smooth domain in \(\mathbb
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Existence of solutions of nonlinear systems subject to arbitrary linear non-local boundary conditions J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2023-10-05 Alberto Cabada, Lucía López-Somoza, Mouhcine Yousfi
In this paper, we obtain an explicit expression for the Green’s function of a certain type of systems of differential equations subject to non-local linear boundary conditions. In such boundary conditions, the dependence on certain parameters is considered. The idea of the study is to transform the given system into another first-order differential linear system together with the two-point boundary
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Geodesics of norms on the contactomorphisms group of $${\mathbb {R}}^{2n}\times S^1$$ J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2023-09-16 Pierre-Alexandre Arlove
We prove that some paths of contactomorphisms of \({\mathbb {R}}^{2n}\times S^1\) endowed with its standard contact structure are geodesics for different norms defined on the identity component of the group of compactly supported contactomorphisms and its universal cover. We characterize these geodesics by giving conditions on the Hamiltonian functions that generate them. For every norm considered
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The rigid-flexible value for symplectic embeddings of four-dimensional ellipsoids into polydiscs J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2023-08-24 Alvin Jin, Andrew Lee
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Concepts of almost periodicity and ergodic theorems in locally convex spaces J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2023-08-16 Fardin Amini, Shahram Saeidi
We wish to investigate mean ergodic theorems for generalizations of almost periodic functions on semigroups, as well as for semigroups of operators in the framework of locally convex spaces. Specially, we present functional characterizations of concepts of almost periodicity for vector-valued functions.
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Normalized solutions to nonlocal Schrödinger systems with $$L^2$$ -subcritical and supercritical nonlinearities J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2023-08-14 Jiaqing Hu, Anmin Mao
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Sufficient conditions for perturbations to define the resolvent of the equilibrium problem on complete geodesic spaces J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2023-08-05 Yasunori Kimura, Kazuya Sasaki
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Application of Tikhonov fixed point theorem to analyze an inverse problem for a bioconvective flow model J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2023-08-04 Aníbal Coronel, Alex Tello, Fernando Huancas, Marko Rojas-Medar
In this paper, we study the inverse problem of determining the density function modeling the vector external source for the linear momentum of particles, in a mathematical model for the bioconvective flow problem. The model consists of three equations: linear momentum of particles, a conservation law for the microorganisms, and the incompressibility condition. We analyze the direct problem obtaining
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Fixed point theorem for mappings contracting perimeters of triangles J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2023-08-01 Evgeniy Petrov
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Variational formulae of some functionals by the modified Schouten tensor J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2023-08-01 Guangyue Huang, Bingqing Ma, Qianyu Zeng
In this paper, we mainly study variational formulae of functionals determined by the k-curvature of the modified Schouten tensor which is defined on the space \({\mathcal {G}}(M)\) of Riemannian metrics on a compact manifold M. Firstly, we consider the functional \({\mathcal {F}}_k^{\tau }\) given by $$\begin{aligned} {\mathcal {F}}_k^{\tau }(g): =V^{-\frac{n-2k}{n}} \int \limits _M\sigma _k(P^{\tau
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Existence of positive solutions for one dimensional Minkowski curvature problem with singularity J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2023-07-24 Tingzhi Cheng, Xianghui Xu
In this paper, we consider the existence of positive solutions for one dimensional Minkowski curvature problem with either singular weight function or singular nonlinear term. By virtue of fixed point arguments and perturbation technique, we establish the new existence results of positive solutions under different assumptions on the nonlinear term. Moreover, some examples are also given as applications
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On asymptotically almost periodic solutions to the Navier–Stokes equations in hyperbolic manifolds J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2023-07-19 Pham Truong Xuan, Nguyen Thi Van
In this paper, we study the forward asymptotically almost periodic (AAP-) mild solutions of Navier–Stokes equations on the real hyperbolic manifold \(\mathcal {M}=\mathbb {H}^d(\mathbb {R})\) with dimension \(d \geqslant 2\). Using the dispersive and smoothing estimates for the Stokes equation, we invoke the Massera-type principle to prove the existence and uniqueness of the AAP- mild solution for
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An infinite dimensional version of the intermediate value theorem J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2023-07-12 Pierluigi Benevieri, Alessandro Calamai, Massimo Furi, Maria Patrizia Pera
Let \(\mathfrak {f}= I-k\) be a compact vector field of class \(C^1\) on a real Hilbert space \(\mathbb {H}\). In the spirit of Bolzano’s Theorem on the existence of zeros in a bounded real interval, as well as the extensions due to Cauchy (in \(\mathbb {R}^2\)) and Kronecker (in \(\mathbb {R}^k\)), we prove an existence result for the zeros of \(\mathfrak {f}\) in the open unit ball \(\mathbb {B}\)
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A generalization of the Goebel–Kirk fixed point theorem for asymptotically nonexpansive mappings J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2023-07-06 Janusz Matkowski
Some results extending the Goebel–Kirk fixed point theorem for asymptotically nonexpansive mappings are presented.
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Circle actions on 6-dimensional oriented manifolds with 4 fixed points J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2023-06-23 Donghoon Jang
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On nonsymmetric theorems for coincidence of multi-valued map J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2023-06-19 Allan Edley Ramos de Andrade, Northon Canevari Leme Penteado, Sergio Tsuyoshi Ura
Given a finite group G which acts freely on \(\mathbb {S}^{n}\), H a normal cyclic subgroup of prime order, in de Mattos and dos Santos (Topol. Methods Nonlinear Anal. 33:105–120, 2009) have defined and estimate the cohomological dimension of the set \(A_{\varphi }(f, H, G)\) of (H, G)-coincidence points of a continuous map \(f: X \rightarrow Y\) relative to an essential map \(\varphi : X \rightarrow
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Characterizations of the existence of solutions for variational inequality problems in Hilbert spaces J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2023-06-20 Carlos Alberto Hernández-Linares, Eduardo Martínez-Anteo, Omar Muñiz-Pérez
In this work, we give necessary and sufficient conditions for the existence of solutions to the variational inequality problem: find \(x_0 \in K\) such that \(\langle F(x_0),y-x_0 \rangle \ge 0\), for every \(y \in K\), where K is a nonempty closed convex subset of a real Hilbert space H and \(F:K \rightarrow H\) is a monotone and continuous operator. These characterizations are given in terms of approximate
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Construction of blow-up solution for 5-dimensional critical Fujita-type equation with different blow-up speed J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2023-06-21 Liqun Zhang, Jianfeng Zhao
We are concerned with the blow-up solutions of the 5-dimensional energy critical heat equation \(u_t=\Delta u + | u |^{\frac{4}{3}}u\). Our main finding is to show that the existence of type II solutions results in blowing up at any k points, with arbitrary k blow-up rates. We have employed the inner–outer gluing method to accomplish this.
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Properties of the minimizers for a constrained minimization problem arising in fractional NLS system J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2023-06-19 Lintao Liu, Yan Pan, Haibo Chen
In this paper, we study a fractional NLS system with trapping potentials in \({\mathbb {R}}^{2}\). By constructing a constrained minimization problem, we show that minimizers exist for the minimization problem if and only if the attractive interaction strength \(a_{i}
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Weak solvability of the initial-boundary value problem for inhomogeneous incompressible Kelvin–Voigt fluid motion model of arbitrary finite order J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2023-06-09 Victor Zvyagin, Mikhail Turbin
The aim of the work is to prove the existence of a weak solution to the initial-boundary value problem for an inhomogeneous incompressible Kelvin–Voigt fluid motion model of an arbitrary finite order. To do this, the paper derives a system of equations corresponding to the considered model. After that, the initial-boundary value problem for the considered model in a bounded domain in 2D and 3D cases
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Strong surjections from two-complexes with odd order top-cohomology onto the projective plane J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2023-06-03 Marcio Colombo Fenille, Daciberg Lima Gonçalves, Oziride Manzoli Neto
Given a finite and connected two-dimensional CW complex K with fundamental group \(\Pi \) and second integer cohomology group \(H^2(K;\mathbb {Z})\) finite of odd order, we prove that: (1) for each local integer coefficient system \(\alpha :\Pi \rightarrow \textrm{Aut}(\mathbb {Z})\) over K, the corresponding twisted cohomology group \(H^2(K;_{\alpha }\!\mathbb {Z})\) is finite of odd order, we say
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Nielsen–Borsuk–Ulam number for maps between tori J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2023-06-03 Givanildo Donizeti de Melo, Daniel Vendrúscolo
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Orientability through the algebraic multiplicity J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2023-05-30 Julián López-Gómez, Juan Carlos Sampedro
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Loop coproduct in Morse and Floer homology J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2023-05-26 Kai Cieliebak, Nancy Hingston, Alexandru Oancea
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The Verlinde traces for $$SU_{X}(2,\xi )$$ and blow-ups J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2023-05-22 Israel Moreno-Mejía, Dan Silva-López
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Existence of a positive hyperbolic Reeb orbit in three spheres with finite free group actions J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2023-05-19 Taisuke Shibata
Let \((Y,\lambda )\) be a non-degenerate contact three manifold. D. Cristfaro–Gardiner, M. Hutchings, and D. Pomerleano showed that if \(c_{1}(\xi =\textrm{Ker}\lambda )\) is torsion, then the Reeb vector field of \((Y,\lambda )\) has infinity many Reeb orbits; otherwise, \((Y,\lambda )\) is a lens space or three sphere with exactly two simple elliptic orbits. In the same paper, they also showed that
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Existence and properties of bubbling solutions for a critical nonlinear elliptic equation J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2023-05-18 Chunhua Wang, Qingfang Wang, Jing Yang
We study the following nonlinear critical elliptic equation $$\begin{aligned} -\Delta u+\epsilon Q(y)u=u^{\frac{N+2}{N-2}},\;\;\; u>0\;\;\;\hbox { in } {\mathbb {R}}^N, \end{aligned}$$ where \(\epsilon >0\) is small and \(N\ge 5.\) Assuming that Q(y) is periodic in \(y_1\) with period 1 and has a local minimum at 0 satisfying \(Q(0)>0,\) we prove the existence and local uniqueness of infinitely many
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Seiberg–Witten Floer spectra and contact structures J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2023-05-06 B. R. S. Roso
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Coisotropic Hofer–Zehnder capacities of convex domains and related results J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2023-04-26 Rongrong Jin, Guangcun Lu
We prove representation formulas for the coisotropic Hofer–Zehnder capacities of bounded convex domains with special coisotropic submanifolds and the leaf relation (introduced by Lisi and Rieser recently), study their estimates and relations with the Hofer–Zehnder capacity, give some interesting corollaries, and also obtain corresponding versions of a Brunn-Minkowski type inequality by Artstein–Avidan
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Most continuous and increasing functions on a compact real interval have infinitely many different fixed points J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2023-04-24 Simeon Reich, Alexander J. Zaslavski
We study the space of all continuous and increasing self-mappings of a real interval [a, b], where \(a
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Liouville-type theorem for a nonlinear sub-elliptic system involving $$\Delta _\lambda $$ -Laplacian and advection terms J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2023-04-10 Anh Tuan Duong, Dao Trong Quyet, Nguyen Van Biet
In this paper, we are concerned with the following system: $$\begin{aligned} {\left\{ \begin{array}{ll}-w\Delta _\lambda u-\nabla _\lambda w.\nabla _\lambda u=\rho v^p\\ -w\Delta _\lambda v-\nabla _\lambda w.\nabla _\lambda v=\rho u^q\end{array}\right. } \text{ in } {\mathbb {R}}^N, \end{aligned}$$ where \(w,\rho \) are nonnegative continuous functions satisfying some growth conditions at infinity
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Stability and instability of standing-wave solutions to one-dimensional quadratic-cubic Klein–Gordon equations J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2023-04-04 Daniele Garrisi
We study the stability of standing-waves solutions to a scalar non-linear Klein–Gordon equation in dimension one with a quadratic-cubic non-linearity. Orbits are obtained by applying the semigroup generated by the negative complex unit multiplication on a critical point of the energy constrained to the charge.
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Existence and convergence of solutions for p-Laplacian systems with homogeneous nonlinearities on graphs J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2023-04-01 Mengqiu Shao
In this paper, we investigate a class of p-Laplacian systems on a locally finite graph \(G=(V,E)\). By exploiting the method of Nehari manifold and some new analytical techniques, under suitable assumptions on the potentials and nonlinear terms, we prove that the p-Laplacian system admits a ground state solution \((u_{\lambda },v_{\lambda })\) when the parameter \(\lambda \) is sufficiently large.
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A companion preorder to G-majorization and a Tarski type fixed-point theorem section: convex analysis J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2023-03-30 Marek Niezgoda
In this paper, a companion preorder \( \prec _G^\textrm{comp}\,\) to G-majorization \( \prec _G \) of Eaton type is introduced and studied. Attention is paid to the case of effective groups G. A criterion for G-majorization inequalities to hold is established by utilizing that companion preorder. A characterization of Gateaux differentiable \( \prec _G^\textrm{comp}\,\)-increasing functions is provided
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Cuplength estimates for periodic solutions of Hamiltonian particle-field systems J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2023-03-10 Oliver Fabert, Niek Lamoree
We consider a natural class of time-periodic infinite-dimensional nonlinear Hamiltonian systems modelling the interaction of a classical mechanical system of particles with a scalar wave field. When the field is defined on a space torus \({\mathbb {T}}^d={\mathbb {R}}^d/(2\pi {\mathbb {Z}})^d\) and the coordinates of the particles are constrained to a submanifold \(Q\subset {\mathbb {T}}^d\), we prove
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Generalized Halpern iteration with new control conditions and its application J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2023-02-24 Hai Yu, Fenghui Wang
In this paper, we investigate the generalized Halpern iteration for computing fixed points of nonexpansive mappings in Hilbert space setting, and prove the strong convergence under new control conditions on parameters. The convergence results generalize the existing ones in the literature. We also present a convergence rate analysis for the generalized Halpern iteration with a particular choice of
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Disk potential functions for quadrics J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2023-02-24 Yoosik Kim
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$$L^\infty (\Omega )$$ a priori estimates for subcritical semilinear elliptic equations with a Carathéodory non-linearity J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2023-02-06 Rosa Pardo
We consider a semilinear boundary value problem \( -\Delta u= f(x,u),\) in \(\Omega ,\) with Dirichlet boundary conditions, where \(\Omega \subset {\mathbb {R}}^N \) with \(N> 2,\) is a bounded smooth domain, and f is a Carathéodory function, superlinear and subcritical at infinity. We provide \(L^\infty (\Omega )\) a priori estimates for weak solutions in terms of their \(L^{2^*}(\Omega )\)-norm,
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Global structure of positive solutions for a Neumann problem with indefinite weight in Minkowski space J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2023-01-30 Ruyun Ma, Xiaoxiao Su, Zhongzi Zhao
We show the global structure of positive solutions for the Neumann problem involving mean curvature operator $$\begin{aligned} \left\{ \begin{array}{ll} -(\frac{u'}{\sqrt{1-u'^2}})'=\lambda a(r)f(u), &{}\quad r\in (0,R), \\ u'(0)=u'(R)=0,&{} \\ \end{array} \right. \end{aligned}$$(P) where \(\lambda >0\) is a parameter, \(a:[0,R]\rightarrow {\mathbb {R}}\) is an \(L^1\)-function which is allowed to
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Fixed points and steady solitons for the two-loop renormalization group flow J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2023-01-26 E. García-Río, R. Mariño-Villar, M. E. Vázquez-Abal, R. Vázquez-Lorenzo
Solitons for the two-loop renormalization group flow are studied in the four-dimensional homogeneous setting, providing a classification of algebraic steady four-dimensional solitons.
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Sharp systolic inequalities for rotationally symmetric 2-orbifolds J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2023-01-04 Christian Lange, Tobias Soethe
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The time-periodic problem of the viscous Cahn–Hilliard equation with the homogeneous Dirichlet boundary condition J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2023-01-03 Keiichiro Kagawa, Mitsuharu Ôtani
In this paper, we show the existence and uniqueness of time-periodic solutions for the viscous Cahn–Hilliard equation with the homogeneous Dirichlet boundary condition. We also investigate the asymptotic limit of time-periodic solutions of the viscous Cahn–Hilliard equation to time-periodic solutions of the Allen–Cahn equation or the Cahn–Hilliard equation. We here assume that the nonlinear term can
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Method of alternating projections for the general absolute value equation J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2023-01-03 Jan Harold Alcantara, Jein-Shan Chen, Matthew K. Tam
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The Brouwer fixed point theorem and periodic solutions of differential equations J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2022-12-29 José Ángel Cid, Jean Mawhin
The Brouwer fixed point theorem is a key ingredient in the proof that a periodic differential equation has a periodic solution in a set that satisfies a suitable tangency condition on its boundary. The main goal of this note is to show that both results are in fact equivalent.
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Bifurcations from degenerate orbits of solutions of nonlinear elliptic systems J. Fixed Point Theory Appl. (IF 1.8) Pub Date : 2022-12-26 Anna Gołȩbiewska, Joanna Kluczenko, Piotr Stefaniak
The aim of this paper is to study global bifurcations of non-constant solutions of some nonlinear elliptic systems, namely the system on a sphere and the Neumann problem on a ball. We study the bifurcation phenomenon from families of constant solutions given by critical points of the potentials. Considering this problem in the presence of additional symmetries of a compact Lie group, we study orbits