On ground state solutions for superlinear Hamiltonian elliptic systems

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• 作者：Leiga Zhao (1)
  Fukun Zhao (2)
  
• 关键词：35J60 ; 58E05 ; Elliptic system ; Ground state solution ; Linking
• 刊名：Zeitschrift f眉r angewandte Mathematik und Physik
• 出版年：2013
• 出版时间：June 2013
• 年：2013
• 卷：64
• 期：3
• 页码：403-418
• 全文大小：300KB
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• 作者单位：Leiga Zhao (1)
  Fukun Zhao (2)
  
  1. Department of Mathematics, Beijing University of Chemical Technology, Beijing, 100029, People’s Republic of China
  2. Department of Mathematics, Yunnan Normal University, Kunming, 650092, People’s Republic of China
  
• ISSN：1420-9039

文摘

In this paper, we study the following Hamiltonian elliptic systems $$\left\{\begin{array}{ll}-\Delta u+V(x)u= g(x,v),\quad {\rm in }\, \mathbb{R}^N,\\-\Delta v+V(x)v= f(x,u),\quad {\rm in } \, \mathbb{R}^N.\end{array}\right.$$ where ${V(x)\in C(\mathbb R^N), f(x,t), g(x,t)\in C(\mathbb{R}^N\times \mathbb{R})}$ are superlinear in t at infinity. Without Ambrosetti–Rabinowtitz condition, the existences of ground state solutions are obtained via the combination of generalized linking theorem and monotonicity method.