Acta mathematica scientia,Series B ›› 1998, Vol. 18 ›› Issue (2): 186-196.

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ON NEUMANN PROBLEM FOR SOME SEMILINEAR ELLIPTIC EQUATIONS INVOLVING CRITICAL SOBOLEV EXPONENTS

Xie Ziqing1,2   

  1. 1. The Young Scientist Labortary of Mathematical Physics, Wuhan Institute of Mathematical Sciences, Academia Sinica Wuhan 430071, China;
    2. Department of Mathematic, Hunan Normal University, Changsha 410081, China
  • Received:1996-04-23 Online:1998-06-25 Published:1998-06-25

Abstract: This paper is concerned with Neumann problem for semilinear elliptic equations involving Sobolev critical exponents with limit nonlinearity in boundary condition. By critical point theory and dual variational principle, the author obtains the existence and multiplicity results.

Key words: Neumann problem, semilinear elliptic equation, positive solution, multiplicity of solutions

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