Journal of South China University of Technology (Natural Science Edition) ›› 2006, Vol. 34 ›› Issue (11): 105-108.

• Mathematical Sciences • Previous Articles     Next Articles

Positive Solution to Asymptotically with M ultiple Critical Linear Elliptic Equation Potentials

Shen Yao-tian1  Liu Ai-rong1  Zhai Yong-hong2   

  1. 1.School of Mathematical Sciences,South China Univ.of Tech.,Guangzhou 510640,Guangdong,China;2.Guangzhou Anxun Economic Development Co.,Ltd.,Guangzhou 510420,Guangdong,China
  • Received:2005-12-13 Online:2006-11-25 Published:2006-11-25
  • Contact: 沈尧天(1938-)，男，教授，博士生导师，主要从事椭圆型偏微分方程研究 E-mail:maytshen@scut.edu.en
  • About author:沈尧天(1938-)，男，教授，博士生导师，主要从事椭圆型偏微分方程研究
  • Supported by:

    国家自然科学基金资助项目(10471047)

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Abstract:

This paper discusses the existence of the positive solution to an asymptotically linear elliptic equation with muhiple critical potentials in Sobolev,Hardy space.As the fight term of the equation is asymptotically linear and does not satisfy the Ambrosetti-Rabinowitz condition,the Mountain Pass Theorem without Palais-Smale condition is used to prove that the equation is of at least one positive solution in a weaker condition.

Key words: Mountain Pass Theorem, asymptotical linearity, elliptic equation, positive solution, existence, strong convergence