Acta mathematica scientia,Series A ›› 2013, Vol. 33 ›› Issue (1): 174-184.

• Articles • Previous Articles    

Existence and Multiplicity of Nonnegative Solutions for a Quasilinear System in RN

 ZHANG Wen-Li1, ZHONG Li-Nan2**   

  1. 1.Department of Mathematics, Changzhi University, Shanxi Changzhi |046011;
    2.Department of Mathematics, College of Science, Yanbian University, Jilin Yanji 133002
  • Received:2011-11-30 Revised:2012-12-08 Online:2013-02-25 Published:2013-02-25
  • Contact: ZHONG Li-Nan, E-mail:ywl6133@126.com; zhonglinan2000@126.com
  • Supported by:

    国家自然科学基金(10771105)和山西省高校科技研究开发项目(20111129)资助

Abstract:

In this paper, we consider a class of quasilinear elliptic equations in RN by the minimax theorems and the Ljusternik-Schnirelmann
theory. When 2≤p, q<N, α≥0 and β≥0 satisfy the conditions of α+β+2>max{p, q} and α+1/p*+β+1/q* ≤1, the quasilinear system has at least catMδ(M)  nonnegative solutions by relating the number of solutions with the topology of the set where V and W attain its minimum.

Key words: Quasilinear system,  Nehari manifold, Minimax theorems, Ljusternik-Schnirelmann theory

CLC Number: 

  • 34B15
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