Journal of South China University of Technology (Natural Science Edition) ›› 2009, Vol. 37 ›› Issue (7): 142-146.

• Mathematics • Previous Articles    

Nonlinear Biharmonic Problem with Critical Potential and Indefinite Potential

Zhang Yi-min  Shen Yao-tian   

  1. Department of Mathematics, South China University of Technology, Guangzhou 510640, Guangdong, China
  • Received:2008-06-30 Revised:2009-01-06 Online:2009-07-25 Published:2009-07-25
  • Contact: 张贻民（1980-），男，茂名学院数学系教师，博士生，主要从事微分方程及其应用研究． E-mail:zhangym802@1263.com
  • About author:张贻民（1980-），男，茂名学院数学系教师，博士生，主要从事微分方程及其应用研究．
  • Supported by:

    国家自然科学基金资助项目（10771074）

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Abstract:

This paper deals with a class of nonlinear biharmonic problem with critical potential and indefinite potential in R4. In the investigation, the exponent in critical potential is proved optimal, and the existence of the nontrivial solution is proved by using an optimal Hardy inequality and the character of the first eigenvalue.

Key words: subcritical growth, Hardy inequality, critical potential