Proportionality of Components, Liouville Theorems and a Priori Estimates for Noncooperative Elliptic Systems

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• 作者：Alexandre Montaru (1)
  Boyan Sirakov (2)
  Philippe Souplet (1)
  
• 刊名：Archive for Rational Mechanics and Analysis
• 出版年：2014
• 出版时间：July 2014
• 年：2014
• 卷：213
• 期：1
• 页码：129-169
• 全文大小：
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• 作者单位：Alexandre Montaru (1)
  Boyan Sirakov (2)
  Philippe Souplet (1)
  
  1. Université Paris 13, Sorbonne Paris Cité, LAGA, CNRS, UMR 7539, 93430, Villetaneuse, France
  2. Departamento de Matematica, PUC-Rio, Rua Marquês de S?o Vicente 225, Gávea, Rio de Janeiro, CEP 22451-900, Brazil
  
• ISSN：1432-0673

文摘

We study qualitative properties of positive solutions of noncooperative, possibly nonvariational, elliptic systems. We obtain new classification and Liouville type theorems in the whole Euclidean space, as well as in half-spaces, and deduce a priori estimates and the existence of positive solutions for related Dirichlet problems. We significantly improve the known results for a large class of systems involving a balance between repulsive and attractive terms. This class contains systems arising in biological models of Lotka–Volterra type, in physical models of Bose–Einstein condensates and in models of chemical reactions.