Journal of South China University of Technology (Natural Science Edition) ›› 2006, Vol. 34 ›› Issue (7): 120-123.

• Mathematical Sciences • Previous Articles     Next Articles

Existence of Infinitely Many Solutions to p-Laplacian Equation

Shen Yao-tian  Li Zhou-xin   

  1. College of Mathematical Sciences,South China Univ.of Tech.,Guangzhou 510640,Guangdong,China
  • Received:2005-04-28 Online:2006-07-25 Published:2006-07-25
  • Contact: 沈尧天(1938-)，教授，博士生导师，主要从事偏微分方程的研究． E-mail:maytshen@scut.edu.cn
  • About author:沈尧天(1938-)，教授，博士生导师，主要从事偏微分方程的研究．
  • Supported by:

    国家自然科学基金资助项目(10171032)

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Abstract:

This paper considers the solutions to the Dirichlet problem in a class of p-Laplacian equation. In the condition weaker than the(AR)condition,the corresponding functional of the equation is first proved satisfying the (PS)c condition. Then,by applying the Mountain Pass Theorem,the existence of infinitely many solutions of the problem is confirmed.

Key words: p-Laplacian equation, critical point, (PS)c condition, Mountain Pass Theorem