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We study Neumann functions for divergence form, second order elliptic systems with bounded measurable coefficients in a bounded Lipschitz domain or a Lipschitz graph domain. We establish existence, uniqueness, and various estimates for the…

Analysis of PDEs · Mathematics 2014-09-25 Jongkeun Choi , Seick Kim

In this paper, we investigate the following nonlinear Schr\"odinger equation with Neumann boundary conditions: \begin{equation*} \begin{cases} -\Delta u+ \lambda u= f(u) & {\rm in} \,~ \Omega,\\ \displaystyle\frac{\partial u}{\partial…

Analysis of PDEs · Mathematics 2025-03-21 Xiaojun Chang , Vicenţiu D. Rădulescu , Yuxuan Zhang

In this work we deal with elliptic equations driven by the variable exponent double phase operator with a Kirchhoff term and a right-hand side that is just locally defined in terms of very mild assumptions. Based on an abstract critical…

Analysis of PDEs · Mathematics 2023-07-17 Ky Ho , Patrick Winkert

We study a Klein-Gordon-Maxwell system, in a bounded spatial domain, under Neumann boundary conditions on the electric potential. We allow a nonconstant coupling coefficient. For sufficiently small data, we find infinitely many static…

Analysis of PDEs · Mathematics 2019-12-03 Monica Lazzo , Lorenzo Pisani

In this paper we consider a generalized fourth order nonlinear Kirchhoff equation in a bounded domain in $\mathbb R^{N}, N\geq2$ under Navier boundary conditions and with sublinear nonlinearity. We employ a change of variable which reduces…

Analysis of PDEs · Mathematics 2017-05-10 João R. Santos Júnior , Gaetano Siciliano

We establish conditions for nonexistence of global solutions for a class of quasilinear parabolic problems with a potential on complete, non-compact Riemannian manifolds, including the Porous Medium Equation and the p-Laplacian with a…

Analysis of PDEs · Mathematics 2025-11-21 Dorothea-Enrica von Criegern , Gabriele Grillo , Dario Monticelli

In this paper, we investigate existence results for nonlinear nonlocal problems governed by an operator obtained as a superposition of fractional $p$-Laplacians, subject to Neumann boundary conditions. A spectral analysis of the main…

Analysis of PDEs · Mathematics 2025-12-16 Yergen Aikyn

In the paper we show that critical sequences associated with the mountain pass level for semilinear elliptic problems on $\R^N$ converge when the non-linearity is subcritical, superlinear and satisfies the penalty condition…

Analysis of PDEs · Mathematics 2007-05-23 Kyril Tintarev

In this paper, we investigate the existence of normalized solutions for the following nonlinear Kirchhoff type problem \begin{equation*} \begin{cases} -(a+b\int_{\Omega}\vert\nabla u\vert^2dx)\Delta u+\lambda u=\vert u\vert^{p-2}u & \text{…

Analysis of PDEs · Mathematics 2024-09-02 Qun Wang , Xiaojun Chang

We consider a slightly subcritical elliptic system with Dirichlet boundary conditions and a non-power nonlinearity in a bounded smooth domain. For this problem, standard compact embeddings cannot be used to guarantee the existence of…

Analysis of PDEs · Mathematics 2023-11-20 Mabel Cuesta , Rosa Pardo , Angela Pistoia

We develop a unified framework for a broad class of nonlocal elliptic problems, encompassing a wide spectrum of nonlocal terms, including the classical Kirchhoff and Carrier-type equations as particular cases, and nonlinearities having…

Analysis of PDEs · Mathematics 2026-03-25 L. Gasinski , H. Ramos Quoirin , J. Santos Junior , K. Silva

Using variational methods, we obtain several multiplicity results for double phase problems that involve variable exponents and a new type of critical growth. This new critical growth is better suited for double phase problems when compared…

Analysis of PDEs · Mathematics 2023-08-15 Hoang Hai Ha , Ky Ho

This paper is concerned with a class of nonhomogeneous quasilinear elliptic system driven by the locally symmetric potential and the small continuous perturbations in the whole-space $\mathbb{R}^N$. By a variant of Clark's theorem without…

Analysis of PDEs · Mathematics 2023-08-14 Cuiling Liu , Xingyong Zhang , Liben Wang

In this paper, we consider the multiplicity of solutions for a class of Kirchhoff type problems with sub-linear and critical terms on an unbounded domain. With the aid of Ekeland's variational principle and the concentration compactness…

Functional Analysis · Mathematics 2016-05-23 Xiaofei Cao , Junxiang Xu , Jun Wang

This paper deals with the existence and multiplicity of solutions for a class of Kirchhoff type elliptic system involving the Trudinger-Moser exponential growth nonlinearities. We first study the existence of solutions for the following…

Analysis of PDEs · Mathematics 2022-10-06 Shengbing Deng , Xingliang Tian

This paper investigates the asymptotic behavior of a class of nonlinear variational problems with Robin-type boundary conditions on a bounded Lipschitz domain. The energy functional contains a bulk term (the $p$-norm of the gradient), a…

Analysis of PDEs · Mathematics 2025-06-10 Giuseppe Buttazzo , Roberto Ognibene

In the paper, we derive an existence result for a nonlinear nonautonomous partial elliptic system on an open bounded domain with Dirichlet boundary conditions, containg fractional powers of the weak Dirichlet-Laplace operator that are meant…

Analysis of PDEs · Mathematics 2019-01-01 Dariusz Idczak

\noi In this article, we study the existence of non-negative solutions of the following polyharmonic Kirchhoff type problem with critical singular exponential nolinearity $$ \quad \left\{ \begin{array}{lr} \quad…

Analysis of PDEs · Mathematics 2016-04-04 Pawan Kumar Mishra , Sarika Goyal , K. Sreenadh

We consider a kind of nonlinear systems on a locally finite graphs $G=(V,E)$. We prove via the mountain pass theorem that this kind of systems has a nontrivial ground state solution which depends on the parameter $\lambda$ with some…

Analysis of PDEs · Mathematics 2021-11-23 Jinyan Xu , Liang Zhao

In this paper, we deal with the existence of nontrivial nonnegative solutions for a $(p, N)$-Laplacian Schr{\"o}dinger-Kirchhoff problem in $\mathbb{R}^N$ with singular exponential nonlinearity. The main features of the paper are the $(p,…

Analysis of PDEs · Mathematics 2023-12-04 Deepak Kumar Mahanta , Tuhina Mukherjee , Abhishek Sarkar