Blow-up for Schrödinger-Poisson critical systems in dimensions 4 and 5

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• 作者：Pierre-Damien Thizy
• 关键词：58J05 ; 35J47 ; 35B09 ; 35B33 ; 49J35 ; 35Q61 ; 35R01 ; 81Q35
• 刊名：Calculus of Variations and Partial Differential Equations
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：55
• 期：1
• 全文大小：617 KB
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• 作者单位：Pierre-Damien Thizy (1)
  
  1. Département de Mathématiques, Université de Cergy-Pontoise, CNRS, 95000, Cergy-Pontoise, France
  
• 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 prove the existence of sequences of smooth positive solutions to the critical Schrödinger-Poisson system which are not bounded in \(H^1\) when the dimension n of the ambient space is 4 and 5. Our results are in striking contrast with the lower dimensional case \(n=3\) and the higher dimensional cases \(n \ge 6\) where, by Hebey and Wei [12] and Thizy [21], no such sequences of solutions exist. The phenomenon we point out in this paper is very particular to dimensions 4 and 5. Mathematics Subject Classification 58J05 35J47 35B09 35B33 49J35 35Q61 35R01 81Q35