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Critical fractional p-Kirchhoff type problem with a generalized Choquard nonlinearity and magnetic field Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2024-04-18 Wenjing Chen, Dongxue Feng
In this article, we establish the fractional version of concentration compactness principle to study the existence of solutions for the critical fractional p-Kirchhoff problem with magnetic field, ...
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L-functions and meromorphic functions satisfying the same Riemann-type functional equation and sharing sets Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2024-04-18 Arpita Kundu, Abhijit Banerjee
In 2023, Li–Du–Yi [Complex Var. Elliptic Equ., 68(10)2023, 1653–1677] proved that if two L-functions L1 and L2 in the extended Selberg class S# have positive degrees, satisfy the same functional eq...
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Iterated Robin problem, the case of various parameters Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2024-04-18 Serkan Emek
Prescribing Robin boundary conditions for the iterated Poisson equation (∂z∂z¯)nw=f leads to Robin-n problems. Extending previous results by allowing an independent choice for the parameters αk,βk ...
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Global structure of positive solutions for a singular quasilinear elliptic problem Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2024-04-17 Ruyun Ma, Lijuan Yang
We are concerned with the existence of positive solutions for the quasilinear problem (P) {−Δpu=λK(|x|)f(u),x∈RN∖B(r0), g~1(u)u−a1∇u⋅x|x|→0,|x|→∞,g~2(u)u+a2∂u∂n=0,x∈∂B(r0), where Δps=div(|∇s|p−2...
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Normalized bound state solutions of fractional Schrödinger equations with general potential Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2024-04-14 Xin Bao, Ying Lv, Zeng-Qi Ou
In this article, we study a class of fractional Schrödinger equation (1) {(−Δ)su=λu+a(x)|u|p−2u,∫RN|u|2dx=c2,u∈Hs(RN), where N>2s, s∈(0,1) and p∈(2,2+4s/N),c>0. a(x)∈C(RN,R) is a positive potent...
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On the Choquard equation with double critical Sobolev exponents in ℝN Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2024-04-12 Zhongyuan Liu, Ziying Liu, Wenhuan Xu
In this paper, we study the existence and nonexistence results to the Choquard equation −Δu=(∫RN|u(y)|2α∗|x−y|αdy)|u|2α∗−2u±|u|q−2uinRN, where 2α∗=2N−αN−2, 0<α
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Improvement of non-integrated defect relation for meromorphic maps from Kähler manifolds Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2024-04-12 Tran Duc Ngoc, Si Duc Quang
The purpose of this paper is to establish a non-integrated defect relation for meromorphic mappings from a complete Kähler manifold into a projective variety intersecting an arbitrary family of hyp...
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Competing Kohn–Spencer Laplacian systems with convection in non-isotropic Folland–Stein space Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2024-04-12 A. Razani
Here, we study the existence of a generalized and a strong generalized solutions of the Dirichlet competing Kohn–Spencer Laplacian with convection problem {−ΔHnp1u+μ1ΔHnq1u=f1(ξ,u,v,DHnu,DHnv),−ΔH...
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On a fractional (p,q)-Laplacian equation with critical nonlinearities Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2024-04-08 Yansheng Shen
In this paper, we consider the following fractional (p,q)-Laplacian equations with critical Hardy-Sobolev exponents {(−Δ)ps1u+(−Δ)qs2u=λ|u|r−2u+μ|u|ps1∗(α)−2u|x|αinΩ,u=0inRN∖Ω, where 0
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Differential subordination of certain class of starlike functions Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2024-03-20 N. Verma, S. Sivaprasad Kumar
This paper presents several results concerning second and third-order differential subordination for the class Se∗:={f∈A:zf′(z)/f(z)≺ez}, which represents the class of starlike functions associated...
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Ground states of biharmonic equations with logarithmic weights and critical exponential growth Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2024-03-05 Imed Abid, Sami Baraket
In this paper, we investigate a fourth-order weighted equation of the form Δ(w(x)|Δu|N2−2Δu)=f(x,u) within the unit ball B of RN. Our focus lies on establishing the existence of solutions under the...
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The dipolar Schramm-Loewner equation for finitely many slits Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2024-02-29 Shi-Yi Lan, Jia Zhang
Let Σ be any disjoint union of finitely many simple curves in the strip region. Based on the continuous dependence of dipolar Loewner chains and the pre-compactness of driving functions associated ...
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Existence of solution for a nonlocal elliptic problem with a Robin-type data Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2024-02-21 Debajyoti Choudhuri, Rana Alkhal, Kamel Saoudi
The aim of this work is to study the elliptic problem: (−Δp)su+|u|p−2u=μf(x,u)+λu−γ in Ω,u>0 in Ω,Npsu+α(x)|u|p−2u=0 in RN∖Ω, under some conditions on the nonlinearity f. Here 2≤p≤ps∗, μ,λ>0, 0
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Nonexistence and multiplicity results for a fractional weighted (p,q)-Kirchhoff system Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2024-02-20 Xiumei Han, Zohreh Naghizadeh, Binlin Zhang
In this article, we study required conditions to guarantee the nonexistence and multiplicity of solutions for a fractional weighted (p,q)-Kirchhoff system by using variational techniques.
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Landau's theorem for harmonic Bloch functions on simply connected domains Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2024-02-14 Vasudevarao Allu, Himadri Halder
For α∈(0,∞), let BH,Ω(α) denote the class of harmonic α-Bloch mappings on a proper simply connected domain Ω⊆C. In this article, we study coefficient estimates for harmonic α-Bloch mappings on a pr...
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On universal quotient Blaschke products Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2024-02-13 Liulan Li, Tao Qian, Shilin Wang
In this paper, we introduce a new member to the universal families, called universal quotient Blaschke product, which is a formal quotient of two formal infinite Blaschke products. A formal infinit...
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A non-local scalar field problem: existence, multiplicity and asymptotic behavior Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2024-02-12 Asma Amira Batahri, Ahmed Attar, Abdelrazek Dieb
The main purpose of this work is to study a non-local scalar field equation in bounded domains. More precisely we consider the semi-linear fractional elliptic problem: (−Δ)su=λup−1−um−1 in Ω,u>0 i...
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Sign-changing solutions for a weighted Kirchhoff problem with exponential growth non-linearity Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2024-02-01 Brahim Dridi, Abir Amor Ben Ali, Rached Jaidane
In this work, we establish the existence of solutions that change sign at low energy for a non-local weighted Kirchhoff problem in the set RN,N>2. The non-linearity of the equation is assumed to ha...
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p(x)-biharmonic equations involving Leray–Lions type operators with Hardy potentials Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2024-02-06 Jian Liu, Zengqin Zhao
In this article, we investigate p(x)-biharmonic equations involving Leray–Lions type operators with Hardy potentials. New criteria for the existence of at least one or at least three generalized so...
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Improvements to the Montel–Carathéodory theorem for families of Pn-valued holomorphic curves Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2024-02-01 Gopal Datt
In this paper, we establish various sufficient conditions for a family of holomorphic mappings on a domain D⊆C into Pn to be normal. Our results are improvements to the Montel–Carathéodory Theorem ...
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Polyanalytic Neumann-n problem in the unit disk Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2024-01-26 Heinrich Begehr
An iterated Neumann boundary value problem for the polyanalytic operator is investigated in the unit disc of the complex plane. Although this problem can be treated for domains in the complex plane...
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A critical phenomenon for the least energy solutions to nonlinear scalar field equations Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2024-01-22 Jun Wang, Xiaoguang Li
We study the existence of least energy solutions to the nonlinear scalar field equation: (1) −Δu+λu+V(x)u=Q(x)|u|pu,u∈H1(RN), Where V(x),Q(x)∈L∞(RN) are real functions satisfying suitable assump...
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A free boundary problem for discontinuous semilinear elliptic equations in convex ring Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2024-01-22 Sabri Bensid
In this paper, we consider the following free boundary problem: (P){Δu=λϕ(x)∑i=1nH(u−μi)inΩ=Ω2∖Ω¯1,u=0on∂Ω2,u=Mon∂Ω1. The domain Ω is a convex ring where Ω1 and Ω2 are bounded convex domains in R...
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Solvability in the sense of sequences for some linear and nonlinear Fredholm operators with the logarithmic Laplacian Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2024-01-24 Messoud Efendiev, Vitali Vougalter
We study the solvability of certain linear and nonlinear nonhomogeneous equations in one dimension involving the logarithmic Laplacian and the transport term. In the linear case we show that the co...
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Embedding model and de Branges-Rovnyak spaces in Dirichlet spaces Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2024-01-03 Carlo Bellavita, Eugenio Dellepiane
In this paper we study embeddings between de Branges-Rovnyak spaces H(b) and harmonically weighted Dirichlet spaces D(μ) in terms of the boundary spectrum of b and the support of the measure μ, by ...
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Riemann boundary value problems on the Archimedean spiral Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-12-28 Shaohua Fan, Hua Liu, ZhiHui Nie
This paper studies the Riemann boundary value problems on the Archimedean spiral. We characterize the functions which are integrable on the Archimedean spiral. We also study the asymptotic behavior...
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Existence of solutions to a critical Kirchhoff equation with logarithmic perturbation Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-12-28 Qi Li, Yuzhu Han
In this paper, the following Kirchhoff type elliptic equation −(a+b∫Ω|∇u|2dx)Δu=λ|u|q−2uln|u|2+|u|4u, which involves a power type nonlinearity with critical Sobolev exponent and a logarithmic ty...
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On existence and concentration of positive solutions for a fractional Kirchhoff equation with critical exponential growth Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-12-27 Ruichang Pei, Jihui Zhang
In this paper we consider the following fractional Kirchhoff type problem {(ϵa+ϵb2π∫R2|u(x)−u(y)|2|x−y|2dxdy)(−Δ)12u+V(x)u=f(u)in R,u∈H1/2(R),u>0in R, where ϵ is a positive parameter and a,b>0 ar...
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The Cauchy integral formula for (p, q)-monogenic functions with α-weight in superspace Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-12-28 Long Gao, Xiaojing Du, Xiaotong Liang, Yonghong Xie
First, some properties for (p,q)-monogenic functions with α-weight in superspace are obtained. Then the Cauchy–Pompeiu formula in superspace is given. Finally, the Cauchy integral formula and the C...
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Weighted composition operators on harmonic Fock spaces Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-12-26 Pham Viet Hai
In this paper, we study weighted composition operators on Fock spaces of harmonic functions (briefly as harmonic Fock spaces). The basic properties of such operators (boundedness, compactness, inve...
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Multiple solutions for the logarithmic fractional Kirchhoff equation with critical or supercritical nonlinearity Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-12-21 Ting Huang, Yan-Ying Shang
In this paper, we study the following logarithmic fractional Kirchhoff equation: (a+b∫R3|(−Δ)s/2u|2dx)(−Δ)su+V(x)u=|u|p−2ulogu2+λ|u|q−2u,inR3, where a, b>0, (−Δ)s is the fractional Laplace opera...
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Eigenoscillations of the Maxwell equation in a domain with oscillating boundary Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-12-21 Siwar Saidani, Abdessatar Khelifi
We consider the eigenfrequency problem of the magnetic field of Maxwell's equation in a domain Ω of R3 with an inclusion O under perturbation Oδ, which is a thin layer at the wall boundary (skin de...
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On Clifford multivector-valued actions, generalized Dirac equation and quantization of branes Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-12-21 Carlos Castro Perelman
We explore the construction of a generalized Dirac equation via the introduction of the notion of Clifford multivector-valued actions, which was inspired by the work of Kanatchikov [Kanatchikov IV....
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A Kohn–Nirenberg type domain in Cn Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-12-14 Junmin Han, Xi Wu, Di Zhao
In this paper, we consider a Kohn–Nirenberg type domain Ω={(z1,…,zn)∈Cn:Rezn+∑j=1n−1(|zj|p+Kj|zj|p−qRezjq+Lj|zj|p−qImzjq)<0} and discuss the existence of supporting surface and peak function at the...
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Mixed local and nonlocal elliptic equation with singular and critical Choquard nonlinearity Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-12-14 G.C. Anthal, J. Giacomoni, K. Sreenadh
In this article, we study a class of elliptic problems involving both local and nonlocal operators with different orders and a singular nonlinearity in combination with critical Hartree type nonlin...
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Homogenization and corrector result of optimal control problem for Stokes system Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-12-14 Ritu Raj, Bidhan Chandra Sardar
This article introduces the boundary optimal control problem in an N-dimensional domain governed by the stationary Stokes equations. Controls are applied to the states through Neumann data on the b...
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A generalization of squeezing function Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-12-03 Abdelwahed Chrih, Youssef Khelifi
In this article, we introduce a new generalized squeezing function defined on bounded domains in Cn and we describe its properties. We compare our generalized squeezing function with the squeezing ...
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Infinitely many solutions for problems involving -Laplacian and -biharmonic operators Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-12-01 Abdelhakim Sahbani
In this paper, we study by using variational methods, mountain pass theorem, Z2-mountain pass theorem combined with the theory of the generalized Lebesgue Sobolev spaces, the existence and multipli...
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Oversampling on a class of symmetric regular de Branges spaces Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-11-30 Luis O. Silva, Julio H. Toloza
A de Branges space B is regular if the constants belong to its space of associated functions and is symmetric if it is isometrically invariant under the map F(z)↦F(−z). Let KB(z,w) be the reproduci...
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Fractional magnetic Schrödinger equations with potential vanishing at infinity and supercritical exponents Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-11-29 J.C. de Albuquerque, J.L. Santos
This paper focuses on the following class of fractional magnetic Schrödinger equations: (−Δ)Asu+V(x)u=g(|u|2)u+λ|u|q−2u,in RN, where (−Δ)As is the fractional magnetic Laplacian, A:RN→RN is the ma...
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Multiplicity of solutions for a scalar field equation involving a fractional p-Laplacian with general nonlinearity Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-11-20 H. P. Bueno, O. H. Miyagaki, A. L. Vieira
We prove the existence of infinitely many radially symmetric solutions to the problem (−Δp)su=g(u)inRN,u∈Ws,p(RN), where s∈(0,1), 2≤p<∞, sp≤N, 2≤N∈N and (−Δp)s is the fractional p-Laplacian opera...
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On the total length of Gamma-lines for rational functions Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-11-14 Yi C. Huang, Jian-Yang Zhang
In this paper, we present a simple direct proof of an integration lemma due to Barsegian, Sergeev and Montes-Rodrigues, and extend to rational functions their upper estimates on the total length of...
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Application of hypergeometric functions to the construction of particular solutions Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-11-05 B. Y. Irgashev
In this article, by the similarity method, self-similar solutions of higher-order equations with constant and variable coefficients are constructed. Self-similar solutions are expressed in terms of...
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The weighted reproducing kernels of the Reinhardt domain Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-10-30 Qian Fu, Guantie Deng
In this paper, we develop the theory of weighted Bergman space and obtain a general representation formula of the Bergman kernel function for the spaces on the Reinhardt domain containing the origi...
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Nonlinear polyharmonic boundary value problems in the punctured unit ball Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-10-13 Zeineb Ben Yahia, Zagharide Zine El Abidine
In this paper we investigate the existence and the asymptotic behavior of positive continuous solutions for a class of nonlinear polyharmonic boundary value problems in the punctured unit ball of R...
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On the higher order Kobayashi pseudometric Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-10-11 Seok Ban, Florian Bertrand, Amir Jaber Chehayeb, Adam Salha, Walid Tabbara
We study the higher order Kobayashi pseudometric introduced by Yu. We first obtain estimates of this pseudometric in a special pseudoconvex domain in C3. We then study the structure of the higher o...
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A class of elliptic problems driven by a mixed local-nonlocal operator Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-10-13 Zijian Wu, Haibo Chen
In this paper, we consider a class of elliptic problems driven by a mixed local-nonlocal operator. By estimating the critical groups and using Morse theory, the existence of nontrivial solutions is...
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Sharp critical exponents for nonlinear equations with the fractional Laplacian Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-10-08 Zixia Yuan, Zimin Tang
In this paper we consider two classes of nonlinear partial differential equations with the fractional Laplacian, namely (−Δ)α2(um)=u|u|q−1+w(x),x∈RN,1≤mα and ∂ku∂tk+(−Δ)α2u=uq,(x,t)...
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The Laurent expansion and residue theorem of weighted monogenic functions Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-10-01 Liping Wang, Liping Luo, Ying Li, Xin Jiang
Firstly, the definition of p order homogeneous weighted right monogenic polynomials is given, and the hypercomplex variables are introduced in order to construct a basis of all homogeneous weighted...
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Some uncertainty principles for the continuous voice transform Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-09-25 Moussa Faress, Said Fahlaoui
In this paper, after recalling the main properties of the voice transform, we prove its inversion formula, then we present some qualitative uncertainty principles associated with this transform. Fi...
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Existence of solution for the (p, q)-fractional Laplacian equation with nonlocal Choquard reaction and exponential growth Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-09-28 Nguyen Van Thin, Pham Thi Thuy, Trinh Thi Diep Linh
In this paper, we study the existence of weak solution to (p,q)-fractional Choquard equation in RN as follows Lpsu+Lqsu+V(x)(|u|p−2u+|u|q−2u)=(1|x|μ∗F(u))f(u), where 2≤Ns=p
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Existence of infinitely many solutions for a class of Schrödinger–Poisson equations without any growth and Ambrosetti–Rabinowitz conditions in RN Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-09-12 Jin-Fu Yang, Jia-Feng Zhang, Wen-Min Li, Qin Qin
In this paper, we study the following kind of Schrödinger–Poisson equations without any growth and Ambrosetti–Rabinowitz conditions: −Δu+V(x)u+(|x|−1∗u2)u−λu=f(u),x∈RN,−Δu+V(x)u+(|x|−1∗u2)u−λu=f(u),x∈RN, where λ<0 , V(x)∈C[0,+∞) is a potential function and satisfies certain conditions. By using variational method, truncation function and Fountain Theorem, we get the existence of infinitely many solutions
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Indefinite Schrödinger equation with nonlinearity sublinear at zero Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-09-07 Shibo Liu, Chunshan Zhao
We consider stationary Schrödinger equations with indefinite potential and nonlinearity sublinear at u = 0. Using linking theorem and symmetric mountain pass theorem, existence and multiplicity results are obtained.
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Singular elliptic problem with super-quadratic growth in the gradient Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-09-03 Siham Boukarabila, Ana Primo, Abdelbadie Younes
ABSTRACT In this paper we analyze the existence of solution to the homogeneous Dirichlet for a nonlinear elliptic singular problem, ⎧⎩⎨⎪⎪−Δu=|∇u|q|u|α+λfu=0inΩ,on∂Ω,{−Δu=|∇u|q|u|α+λfinΩ,u=0on∂Ω, where N≥2N≥2 , Ω⊂RNΩ⊂RN is a bounded regular domain, q>2, α0 and f is a nonnegative function belonging to a suitable Lebesgue space. Under additional hypotheses on the data, we are also able to show the uniqueness
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Existence and multiplicity of solutions for m-polyharmonic Kirchhoff problems without Ambrosetti–Rabinowitz conditions Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-08-30 A. Harrabi, M. K. Hamdani, A. Fiscella
In this paper, we prove the existence of infinitely many solutions for a class of quasilinear elliptic m-polyharmonic Kirchhoff equations where the nonlinear function has a quasicritical growth at infinity and without assuming the Ambrosetti and Rabinowitz type condition. The new aspect consists in employing the notion of a Schauder basis to verify the geometry of the symmetric mountain pass theorem
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Infinitely many nodal solutions for a modified Kirchhoff type equation Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-08-29 Na Liu, Tao Wang
In this paper, we consider the modified Kirchhoff type equation, that is, the Kirchhoff type equation with a quasilinear term (1) ⎧⎩⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪−(a+b∫R3∣∣∣∇u∣∣∣2dx)Δu+V(∣∣∣∣x∣∣∣∣)u−12Δ(∣∣∣∣u∣∣∣∣2)u=∣∣u∣∣p−2uin R3,u→0as |x|→∞,{−(a+b∫R3|∇u|2dx)Δu+V(|x|)u−12Δ(|u|2)u=|u|p−2uin R3,u→0as |x|→∞, (1) where a, b>0, p∈(4,22∗)p∈(4,22∗) and V(|x|)V(|x|) is a radial potential function and bounded below by a positive
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Frequent hypercyclicity of the tensor products of composition operators on weighted Dirichlet spaces Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-08-27 Zhitao Guo
In this paper, we mainly study the frequent hypercyclicity of a scalar multiple of the tensor product of two linear fractional composition operators λCφ⊗CψλCφ⊗Cψ on Sν⊗SνSν⊗Sν , where Sν is the weighted Dirichlet space. We will restrict the discussion to the situations that both φ and ψ are hyperbolic non automorphisms, hyperbolic automorphisms and parabolic automorphisms, respectively. Meanwhile,
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A note on unique continuation of eigenfunctions for p-Laplacian operator in a bounded domain Ω in ℝn with a potential V in Lp(Ω) Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-08-27 René Erlin Castillo
The aim of this note is to study the problem −div(|∇u|p−2∇u)+V|u|p−2u=0−div(|∇u|p−2∇u)+V|u|p−2u=0 in Ω, where Ω is a bounded domain in RnRn and the potential V is assumed to be not equivalent to zero and lies in Lp(Ω). Also, we establish the strong unique continuation property of the eigenfunctions for the p-Laplacian operator in the case where V∈Lp(Ω).
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Correction Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-08-24
Published in Complex Variables and Elliptic Equations: An International Journal (Ahead of Print, 2023)
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Complex boundary value problems on a circular triangle Complex Var. Elliptic Equ. (IF 0.9) Pub Date : 2023-08-23 Hamed Emkanpour, Nasir Taghizadeh
We apply the parqueting-reflection technique for a triangle domain to achieve the points of the complex plane. Then the Cauchy–Schwarz representation formula is construed by the Cauchy–Pompeiu formula and an explicit solution for the Schwarz boundary value problem (BVP) for the non-homogeneous Cauchy–Riemann equation on the triangle is presented. We also discuss the condition of solvability and by