EXISTENCE OF SOLUTIONS FOR A SEMILINEAR ELLIPTIC SYSTEM

被引：6
|
作者：
Benrhouma, Mohamed [1 ]
机构：
[1] Sci Fac Monastir, Dept Math, Monastir 5019, Tunisia
来源：
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS | 2013年 / 19卷 / 02期
关键词：
Semilinear elliptic systems; Nehari manifold; concentration-compactness principle; variational methods; POSITIVE SOLUTIONS; UNIQUENESS; SYMMETRY;
D O I：
10.1051/cocv/2012022
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
This paper deals with the existence of solutions to the following system: {-Delta u + u = alpha/alpha+beta a(x)vertical bar v vertical bar(beta)vertical bar u vertical bar(alpha-2)u in R-N {-Delta v + v = beta/alpha+beta a(x)vertical bar u vertical bar(alpha)vertical bar v vertical bar(beta-2)v R-N. With the help of the Nehari manifold and the linking theorem, we prove the existence of at least two nontrivial solutions. One of them is positive. Our main tools are the concentration- compactness principle and the Ekeland's variational principle.
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页码：574 / 586
页数：13
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