Acta mathematica scientia,Series A ›› 2009, Vol. 29 ›› Issue (3): 727-736.

• Articles • Previous Articles     Next Articles

The Existence of Nontrivial Generalized Solution of a Class of Quasilinear Elliptic Equations

  

  1. (School of Mathematics and Computer Science, Changsha University of Science and Technology, Changsha 410077)
  • Received:2007-09-21 Revised:2008-11-10 Online:2009-06-25 Published:2009-06-25
  • Supported by:

    国家自然科学基金(10671211)资助

Abstract:

In this paper, we study the existence of nontrivial solutions of the following quasilinear elliptic Dirichlet problem in an Orlicz-Sobolev space:

{ -div(a(|     u(x)|)     u(x))=g(x, u),     x ∈ Ω,
  u(x)=0,                                               x ∈ ∂Ω.

where Ω is a bounded domain in Rn. Using the generalized mountain pass lemma, we prove, under some conditions on Φ and g, the existence of nontrivial generalized solutions for this  problem.

Key words: Quasilinear elliptic equation, Orlicz-Sobolev space, Mountain pass lemma, P.S condition

CLC Number: 

  • 35J
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