Radial and nonradial solutions of a strongly indefinite elliptic system on \(\mathbb R ^N\)

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• 作者：Cyril Joel Batkam (1)
  
  1. D茅partement de Math茅matiques ; Universit茅 de Sherbrooke ; Sherbrooke ; QC ; J1K 2R1 ; Canada
  
• 关键词：Radial solutions ; Nonradial solutions ; Noncooperative elliptic system ; Principle of Symmetric Criticality ; Fountain Theorem ; 35A15 ; 35J50
• 刊名：Afrika Matematika
• 出版年：2015
• 出版时间：March 2015
• 年：2015
• 卷：26
• 期：1-2
• 页码：65-75
• 全文大小：186 KB
• 参考文献：1. Ambrosetti, A., Rabinowitz, P.H.: Dual variational methods in critical point theory and applications. J. Funct. Anal. 14, 349鈥?81 (1973)
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  17. Willem, M.: Minimax Theorems. Birkhauser, Boston (1996) CrossRef
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics Education
  Applications of Mathematics
  History of Mathematics
  Mathematics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：2190-7668

文摘

This paper is concerned with the following system of elliptic equations $$\begin{aligned} \left\{ \begin{array}{l} -\Delta u+u= F_u(|x|,u,v),\\ -\Delta v+v=- F_v(|x|,u,v),\\ u,v\in H^1(\mathbb R ^N). \end{array} \right. \end{aligned}$$ It is shown that if \(F\) is even in \((u,v)\) and satisfies some growth conditions, then the system has infinitely many both radial and nonradial solutions. The proof relies on the Principle of Symmetric Criticality and a generalized Fountain Theorem for strongly indefinite even functionals.