数学物理学报(英文版) ›› 2009, Vol. 29 ›› Issue (2): 232-242.doi: 10.1016/S0252-9602(09)60024-2

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SEMILINEAR ELLIPTIC EQUATIONS ON FRACTAL SETS

陈化, 贺振亚   

  1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
  • 收稿日期:2006-09-16 修回日期:2007-07-02 出版日期:2009-03-20 发布日期:2009-03-20
  • 通讯作者: 陈化
  • 基金资助:

    Sponsored by the National NSFC under grant (10631020).

SEMILINEAR ELLIPTIC EQUATIONS ON FRACTAL SETS

Chen Hua, He Zhenya   

  1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
  • Received:2006-09-16 Revised:2007-07-02 Online:2009-03-20 Published:2009-03-20
  • Contact: Chen Hua
  • Supported by:

    Sponsored by the National NSFC under grant (10631020).

摘要:

In this article, the authors consider a class of semilinear elliptic equations on fractal sets under some new conditions, which are more weaker than those in usual cases. The authors get the non-trivial and non-negative solution of the zero boundary Dirichlet problem using Mountain Pass Lemma.

关键词: Fractal, Laplacian operator, semilinear, self-similar, Intrinsic dimension

Abstract:

In this article, the authors consider a class of semilinear elliptic equations on fractal sets under some new conditions, which are more weaker than those in usual cases. The authors get the non-trivial and non-negative solution of the zero boundary Dirichlet problem using Mountain Pass Lemma.

Key words: Fractal, Laplacian operator, semilinear, self-similar, Intrinsic dimension

中图分类号: 

  • 35J20