Semi-classical solutions of perturbed elliptic system with general superlinear nonlinearity

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• 作者：Fangfang Liao (1) (2)
  Xianhua Tang (1)
  Jian Zhang (1)
  Dongdong Qin (1)
  
  1. School of Mathematics and Statistics ; Central South University ; Changsha ; Hunan ; 410083 ; P.R. China
  2. Department of Mathematics ; Xiangnan University ; Chenzhou ; Hunan ; 423000 ; P.R. China
  
• 关键词：35J10 ; 35J20 ; semi ; classical solutions ; perturbed elliptic system ; generalized linking theorems
• 刊名：Boundary Value Problems
• 出版年：2014
• 出版时间：December 2014
• 年：2014
• 卷：2014
• 期：1
• 全文大小：1,248 KB
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• 刊物主题：Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations; Analysis; Approximations and Expansions; Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1687-2770

文摘

This paper is concerned with the following perturbed elliptic system: \(-\varepsilon^{2}\triangle u+V(x)u=W_{v}(x, u, v)\) , \(x\in{\mathbb {R}}^{N}\) , \(-\varepsilon^{2}\triangle v+V(x)v=W_{u}(x, u, v)\) , \(x\in{\mathbb {R}}^{N}\) , \(u, v\in H^{1}({\mathbb{R}}^{N})\) , where \(V \in C({\mathbb{R}}^{N}, {\mathbb{R}})\) and \(W \in C^{1}({\mathbb{R}}^{N}\times\mathbb{R}^{2}, {\mathbb{R}})\) . Under some mild conditions on the potential V and nonlinearity W, we establish the existence of nontrivial semi-classical solutions via variational methods, provided that \(0 , where the bound \(\varepsilon_{0}\) is formulated in terms of N, V, and W.