Infinitely many solutions for superlinear periodic Hamiltonian elliptic systems

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• 作者：Xiaoming Xu (1) (2)
  Qiaoyan Kuang (3)
  Yanping Gong (1)
  
  1. School of Business ; Central South University ; Changsha ; Hunan ; 410083 ; P.R. China
  2. School of Management ; Hunan International Economics University ; Changsha ; Hunan ; 410205 ; P.R. China
  3. School of Information Science and Engineering ; Hunan International Economics University ; Changsha ; Hunan ; 410205 ; P.R. China
  
• 关键词：35J50 ; 35J55 ; Hamiltonian elliptic system ; generalized fountain theorem ; variational methods ; strongly indefinite functionals
• 刊名：Boundary Value Problems
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：2015
• 期：1
• 全文大小：1,220 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 periodic Hamiltonian elliptic system: \(-\Delta u+V(x)u=H_{v}(x,u,v)\) , \(x\in\mathbb{R}^{N}\) , \(-\Delta v+V(x)v=H_{u}(x,u,v)\) , \(x\in\mathbb{R}^{N}\) , \(u(x)\to0\) , \(v(x)\to0\) as \(|x|\to\infty\) . Assuming the potential V is periodic and 0 lies in a gap of \(\sigma(-\Delta+V)\) , \(H(x,z)\) is periodic in x and superquadratic in \(z=(u,v)\) . We establish the existence of infinitely many large energy solutions by the generalized variant fountain theorem developed recently by Batkam and Colin.