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September  2008, 7(5): 1109-1122. doi: 10.3934/cpaa.2008.7.1109

Positive solutions for critical elliptic systems in non-contractible domains

Haiyang He 1, and  Jianfu Yang 2,

1. 

Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, P.O. Box 71010, Wuhan 430071, China
2. 

Department of Mathematics, Jiangxi Normal University, Nanchang, Jiangxi 330022, China

Received  October 2007 Revised  April 2008 Published  June 2008

In this paper, we consider the existence of solutions for a critical elliptic system. We show that the problem possesses at least a high energy positive solution in non-contractible domains.
Keywords: Critical Sobolev exponents, Palais-Smale condition, high energy solution..
Mathematics Subject Classification: Primary: 35J50; Secondary: 35J6.
Citation: Haiyang He, Jianfu Yang. Positive solutions for critical elliptic systems in non-contractible domains. Communications on Pure & Applied Analysis, 2008, 7 (5) : 1109-1122. doi: 10.3934/cpaa.2008.7.1109
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