Journal of South China University of Technology(Natural Science Edition) ›› 2003, Vol. 31 ›› Issue (3): 49-52.

• Mechanical Engineering • Previous Articles     Next Articles

Positive Solution of a Semilinear Elliptic Equation with Critical Exponent 

Yao Yang-xin Chen Zhi-hui Fu Yi-ping Fu Hong-zhuo   

  1. Dept．of Applied Mathematics‚South China Univ．of Tech．‚Guangzhou510640‚China
  • Online:2003-03-20 Published:2022-04-22
  • Contact: Yao Yang-xin （born in 1957）‚male‚associate professor‚mainly researches on partial defferential equation．
  • About author:Yao Yang-xin （born in 1957）‚male‚associate professor‚mainly researches on partial defferential equation．
  • Supported by:
     Supported by the National Natural Science Foundation of China （10171032） and Guangdong Provincial Natural Science Foundation（011606）

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Abstract:  In this paper‚the existence of the positive solution of the follwing semilinear elliptic equation with critical exponent is studied：
－div（｜x｜β ∇ u）＝｜x｜ α u p－1 ＋λ｜x｜ σ u q－1 in Ω‚u＞0in Ω‚u＝0on∂Ω‚
by using Sobolev-Hardy inequality and the Mountain Pass Geometry．

Key words:  semilinear elliptic equation, critical exponent, positive solution, Sobolev-Hardy inequality

CLC Number: