Positive ground states for a system of Schr?dinger equations with critically growing nonlinearities

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• 作者：Pietro d’Avenia ; Jaros?aw Mederski
• 关键词：35J57 ; 35A01 ; 35B33 ; 35J50
• 刊名：Calculus of Variations and Partial Differential Equations
• 出版年：2015
• 出版时间：July 2015
• 年：2015
• 卷：53
• 期：3-4
• 页码：879-900
• 全文大小：539 KB
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• 作者单位：Pietro d’Avenia (1)
  Jaros?aw Mederski (2)
  
  1. Dipartimento di Meccanica, Matematica e Management, Politecnico di Bari, Via Orabona 4, 70125, Bari, Italy
  2. Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, ul. Chopina 12/18, 87-100, Toruń, Poland
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  Systems Theory and Control
  Calculus of Variations and Optimal Control
  Mathematical and Computational Physics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-0835

文摘

We study the following problem $$\begin{aligned} {\left\{ \begin{array}{ll} -\Delta u = \lambda u + u^{2^*-2} v &{}\quad \hbox {in }\quad \Omega ,\\ -\Delta v= \mu v^{2^*-1} + u^{2^*-1} &{}\quad \hbox {in }\quad \Omega ,\\ u> 0,v> 0 &{}\quad \hbox {in }\quad \Omega ,\\ u=v=0 &{}\quad \hbox {on }\quad \partial \Omega , \end{array}\right. } \end{aligned}$$