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

被引：15

作者：

Montaru, Alexandre ^{[1
]}

Sirakov, Boyan ^{[2
]}

Souplet, Philippe ^{[1
]}

机构：

[1] Univ Paris 13, CNRS, Sorbonne Paris Cite, LAGA,UMR 7539, F-93430 Villetaneuse, France

[2] Pontificia Univ Catolica Rio de Janeiro, Dept Matemat, BR-22451900 Rio de Janeiro, Brazil

来源：

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | 2014年 / 213卷 / 01期

关键词：

POSITIVE SOLUTIONS; SCHRODINGER SYSTEMS; EXISTENCE; NONEXISTENCE; DIFFUSION; EQUATIONS; SYMMETRY;

D O I：

10.1007/s00205-013-0719-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：129 / 169

页数：41

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