Hamiltonian elliptic systems in \(\mathbb {R}^2\) with subcritical and critical exponential growth

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• 作者：Manassés de Souza ; João Marcos do Ó
• 刊名：Annali di Matematica Pura ed Applicata
• 出版年：2016
• 出版时间：June 2016
• 年：2016
• 卷：195
• 期：3
• 页码：935-956
• 全文大小：540 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1618-1891
• 卷排序：195

文摘

Our aim in this paper was to establish by a variational method the existence of nontrivial solutions for strongly coupled Hamiltonian systems of the form $$\begin{aligned} \left\{ \begin{array}{llll} -\Delta u +V(x) u&{} = g(x,v), &{}\quad v > 0 &{} \quad \text {in}\; \mathbb {R}^2, \\ -\Delta v +V(x) v&{} = f(x,u), &{}\quad u > 0 &{} \quad \text {in}\; \mathbb {R}^2, \end{array} \right. \end{aligned}$$