Solutions on asymptotically periodic elliptic system with new conditions
type: Item
instance of: scholarly article
title: Solutions on asymptotically periodic elliptic system with new conditions
zbMATH Open document ID: 1358.35032
author: Dongdong Qin
author: X. H. Tang
published in: Results in Mathematics
publication date: 2016-11-29T00:00:00Z
review text: From the abstract: This paper is concerned with the following elliptic system: \[ \begin{cases} -\Delta u+U_{1}(x)u =F_{u}(x,u,v)\quad & \text{in }\mathbb{R}^{N},\\ -\Delta v+U_{2}(x)v=F_{v}(x,u,v) \quad & \text{in }\mathbb{R}^{N},\\ u, \;v \in H^{1}(\mathbb{R}^{N}). \end{cases} \] Assuming that the potential \(U_i(x)\) are periodic in \(x\) and \(0\) lies in a spectral gap of \(\sigma(-\Delta + U_i)\), \(i=1,2\), two types of ground state solutions are obtained with some new super-quadratic conditions on nonlinearity \(F\) which are weaker that some well known ones. For the case that \(U_i(x)\) and \(F(x,u,v)\) are asymptotically periodic in \(x\), a nontrivial solution is established by using a generalized linking theorem and some new techniques.
Mathematics Subject Classification ID: 35J47
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 35J50
zbMATH DE Number: 6657459
zbMATH Keywords: elliptic system
zbMATH Keywords: superlinear
zbMATH Keywords: asymptotically periodic
zbMATH Keywords: ground state
zbMATH Keywords: strongly indefinite functionals
MaRDI profile type: Publication
full work available at URL: s00025-015-0491-x
OpenAlex ID: W2168386496
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DOI: 10.1007/S00025-015-0491-X
description: scientific article; zbMATH DE number 6657459