Journal of South China University of Technology (Natural Science Edition) ›› 2008, Vol. 36 ›› Issue (12): 142-145.

• Mathematics • Previous Articles    

Existence of Solutions to a Class of Biharmonic Equation with Hardy Potential

Wang You-jun  Shen Yao-tian    

  1. Department of Mathematics, South China University of Technology, Guangzhou 510640, Guangdong, China
  • Received:2008-05-27 Revised:2008-08-14 Online:2008-12-25 Published:2008-12-25
  • Contact: 王友军（1981-），男，博士生，主要从事偏微分方程研究． E-mail:youjun3006@126．com
  • About author:王友军（1981-），男，博士生，主要从事偏微分方程研究．
  • Supported by:

    国家自然科学基金资助项目（10471047）;广东自然科学基金资助项目（05300159）

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Abstract:

In this paper, a new Sobolev space is established and a compact embedding theorem is given. Then, the eigenvalue problem of the biharmonic equation with critical exponents is analyzed. Finally, by using the Mountain Pass Lemma satisfying the Cerami condition, the existence of the nontrivial solutions to a class of biharmonic equation with Hardy potential and critical parameter is discussed in the established Sobolev space.

Key words: biharmonic equation, Hardy potential, critical exponent, existence, Cerami condition