Acta mathematica scientia,Series A ›› 2014, Vol. 34 ›› Issue (4): 789-795.

• Articles • Previous Articles     Next Articles

Multiple Solutions for a Semilinear Elliptic Equation Involving Sobolev Critical Exponent

 ZHANG Zheng-Jie, GUO Liu-Tao, ZHU Xiao-Kun   

  1. 1.School of Mathematics and Statistics, Huazhong Normal University, Wuhan 430079;
    2.Editorial Department of Journal, Huazhong Normal University, Wuhan 430079
  • Received:2012-07-12 Revised:2013-11-25 Online:2014-08-25 Published:2014-08-25
  • Supported by:

    国家自然科学基金(11071095, 11371159)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=uN+2/N-2+∈f(x)u,   x∈RN
   uD1,2(RN), u(x)→0, |x|→∞,
where ∈ is a positive constant, f(x)∈L(RN), N>3. Used perturbation method, we prove that under some conditions on f(x), there exists a ∈0, if 0<ε<ε0, such that there are many solutions for above problem.

Key words: Semilinear, Sobolev exponent, Elliptic, Multiple solutions

CLC Number: 

  • 35J60
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