Acta mathematica scientia,Series A ›› 2012, Vol. 32 ›› Issue (5): 833-839.

• Articles • Previous Articles     Next Articles

Multiple Solutions for a kind of Special Semilinear Elliptic Equations

 ZHANG Zheng-Jie, YU Xiao-Ling   

  1. School of Mathematics and Statistics Central China Normal University, Wuhan 430079
  • Received:2011-09-18 Revised:2012-04-17 Online:2012-10-25 Published:2012-10-25
  • Supported by:

    国家自然科学基金和数学物理湖北省重点实验室(华中师范大学)资助

Abstract:

In this paper, we consider the following problem
         {-Δu=(1+εg(x))(u-1)p+,        x∈RN,
        uD1,2(RN),          u(x)→0 ,        |x|→∞,

where ε is a positive constant, g(x)∈L(RN), 1<p<N+2/N-2. Used perturbation method, we prove that under some conditions on g(x), there exists a ε0, if 0<ε<ε0, such that there are many solutions for above problem.

Key words: Semilinear, Elliptic, Multiple solutions

CLC Number: 

  • 35J60
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