Ground State Solutions for Resonant Cooperative Elliptic Systems with General Superlinear Terms
详细信息 查看全文
- 作者：Hongxia Shi ; Haibo Chen
- 关键词：Cooperative elliptic systems ; Superlinear ; Ground state solution
- 刊名：Mediterranean Journal of Mathematics
- 出版年：2016
- 出版时间：October 2016
- 年：2016
- 卷：13
- 期：5
- 页码：2897-2909
- 全文大小：562 KB
- 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics
Mathematics - 出版者：Birkh盲user Basel
- ISSN：1660-5454
- 卷排序：13
文摘
This paper is concerned with the following cooperative elliptic system:$$\left\{\begin{array}{ll}-\Delta u=\xi u+f(x,u,v), \quad \quad \mbox{in }\Omega,-\Delta v=\zeta v+g(x,u,v), \quad \quad \mbox{in }\Omega,u=v=0, \quad \quad\mbox{on }\partial\Omega,\end{array}\right.$$ where \({U=(u,v): \Omega\rightarrow \mathbb{R}^{2}}\), Ω is a bounded smooth domain in \({\mathbb{R}^{N}}\) and \({\xi,\zeta\in\mathbb{R}}\). We establish the existence of ground state solutions for this system using a much more direct approach to find a minimizing Cerami sequence for the energy functional outside the generalized Nehari manifold developed recently by Szulkin and Weth.KeywordsCooperative elliptic systemsSuperlinearGround state solutionThis research was supported by Natural Science Foundation of China 11271372, by the Fundamental Research Funds for the Central Universities of Central South University 2015zzts010 and by the Mathematics and Interdisciplinary Sciences project of CSU.