Acta mathematica scientia,Series A ›› 2016, Vol. 36 ›› Issue (6): 1137-1144.

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Multiple Solutions for Semilinear Elliptic Equations with Critical Exponents and Hardy Potential

Yuan Haihua1, Zhang Zhengjie1, Xu Guojin2   

  1. 1. School of Mathematics and Statistics, Central China Normal University, Wuhan 430079;
    2. School of Mathematics and Statistics, Hubei Engineering University, Hubei Xiaogan 432000
  • Received:2016-03-23 Revised:2016-10-18 Online:2016-12-26 Published:2016-12-26
  • Supported by:

    Supported by the NSFC (11371159) and the Yangtze River Innovation Team of the Ministry Education in Colleges and Universities (IRT13066)

Abstract:

In this paper, we consider the following problem
-△u+(u)/(|x|2)=|u|2*-2u+g(x),x∈RN,
u(x)→0(|x|→∞),uD1,2(RN)
where g(x)≥0,g(x)≠0, 且g(x)∈L(2N)/(N+2)(RN). We can prove that there exists a constant C, which is small enough,such that ‖gL(2N)/(N+2)(RN)C, then there are at least two solutions for the above problem.

Key words: Semi-linear, Hardy potential, Mountain pass lemma

CLC Number: 

  • O175.23
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