Song, Mingliang Chen, Ping
Published in
Advances in Difference Equations

This paper investigates the existence of solutions to subquadratic operator equations with convex nonlinearities and resonance by means of the index theory for self-adjoint linear operators developed by Dong and dual least action principle developed by Clarke and Ekeland. Applying the results to subquadratic convex Hamiltonian systems satisfying se...

Papageorgiou, Nikolaos S. Rădulescu, Vicenţiu D. Repovš, Dušan D.
Published in
Results in Mathematics

We consider a superlinear perturbation of the eigenvalue problem for the Robin Laplacian plus an indefinite and unbounded potential. Using variational tools and critical groups, we show that when λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrs...

Zhang, Wen Zhang, Jian Mi, Heilong
Published in
Advances in Nonlinear Analysis

This paper is concerned with the following nonlinear Hamiltonian elliptic system with gradient term −Δu+b→(x)⋅∇u+V(x)u=Hv(x,u,v)inRN,−Δv−b→(x)⋅∇v+V(x)v=Hu(x,u,v)inRN. $$\begin{array}{} \displaystyle \left\{\,\, \begin{array}{ll} -{\it\Delta} u +\vec{b}(x)\cdot \nabla u+V(x)u = H_{v}(x,u,v)\,\,\hbox{in}\,\mathbb{R}^{N},\\[-0.3em] -{\it\Delta} v -\ve...

Zhang, Jian Chen, Jianhua Li, Quanqing Zhang, Wen
Published in
Advances in Nonlinear Analysis

In this paper, we study the following nonlinear Hamiltonian elliptic system with gradient term −ϵ2Δψ+ϵb→⋅∇ψ+ψ+V(x)φ=f(|η|)φ in RN,−ϵ2Δφ−ϵb→⋅∇φ+φ+V(x)ψ=f(|η|)ψ in RN, $$\begin{array}{} \displaystyle \left\{ \begin{array}{ll} -\epsilon^{2}{\it\Delta} \psi +\epsilon \vec{b}\cdot \nabla \psi +\psi+V(x)\varphi=f(|\eta|)\varphi~~\hbox{in}~\mathbb{R}^{N},...

Abdelwahed, Mohamed Chorfi, Nejmeddine
Published in
Boundary Value Problems

This paper deals with the mathematical analysis of a class of nonlinear eigenvalue problems driven by a nonhomogeneous differential operator. We are concerned both with the coercive and the noncoercive (and nonresonant) cases, which are in relationship with two associated Rayleigh quotients. The proof combines critical point theory arguments and th...

Boumazourh, Athmane Srati, Mohammed
Published in
Moroccan Journal of Pure and Applied Analysis

Via Leray-Schauder’s nonlinear alternative, we obtain the existence of a weak solution for a nonlocal problem driven by an operator of elliptic type in a fractional Orlicz-Sobolev space, with homogeneous Dirichlet boundary conditions.

He, Tieshan He, Lang Zhang, Meng
Published in
Calculus of Variations and Partial Differential Equations

In this paper we consider the quasilinear critical problem -Δpu=λuq-2u+up⋆-2uinΩ,u=0on∂Ω,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \left\{ \begin{...

Pei, Ruichang Ma, Caochuan
Published in
Mediterranean Journal of Mathematics

In this paper, we study a class of Kirchhoff-type equation with asymptotically linear right-hand side and compute the critical groups at a point of mountain pass type under suitable Hilbert space. The existence results of three nontrivial solutions under the resonance and non-resonance conditions are established by using the minimax method and Mors...

Feehan, Paul M. N.
Published in
Calculus of Variations and Partial Differential Equations

It is a consequence of the Morse–Bott Lemma (see Theorems 2.10 and 2.14) that a C2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^2$$\end{document} Morse–Bott functio...

Alsaedi, Ahmed Ahmad, Bashir
Published in
Advances in Nonlinear Analysis

The main purpose of this paper is to study a general class of (p, q)-type eigenvalues problems with lack of compactness. The reaction is a convex-concave nonlinearity described by power-type terms. Our main result establishes a complete description of all situations that can occur. We prove the existence of a critical positive value λ* such that th...