Journal of South China University of Technology (Natural Science Edition) ›› 2007, Vol. 35 ›› Issue (8): 114-117.

• Mathematical Sciences • Previous Articles     Next Articles

Existence of Nontrivial Solution to a Class of Quasi-linear Elliptic Equation

Yao Yang-xin  Zhang Rui-min  Wang Rong-xin   

  1. School of Mathematical Science , South China Univ. of Tech. , Guangzhou 510640 , Guangdong , China
  • Received:2006-07-12 Online:2007-08-25 Published:2007-08-25
  • Contact: 姚仰新(1957-)，男，教授，主要从事偏微分及其应用研究. E-mail:mayxyao@scut. edu.cn
  • About author:姚仰新(1957-)，男，教授，主要从事偏微分及其应用研究.
  • Supported by:

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

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Abstract:

In this paper , the existence of the nontrivial solution to a class of quasi-linear elliptic problem is investigated based on the Hardy inequality and the Mountain Pass Geometry. As the basic solution to the discussed problem is difficult to obtain , an estimation of the basic solution is carried out and the corresponding (PS) c condition is proved.

Key words: quasi -linear elliptic equation, nontrivial solution, existence, (PS) c condition, Mountain Pass Geometry , Hardy inequality