A SOBOLEV-HARDY INEQUALITY WITH APPLICATION TO A NONLINEAR ELLIPTIC EQUATION  

作　　者：Xie Chaodong Wu Yun 

机构地区：[1]Dept. of Economic and Management, Guizhou University for Ethnic Minorties, Guizhou 550025 [2]Dept. of Applied Math., South China University of Technology, Guangzhou 510640

出　　处：《Annals of Differential Equations》2006年第1期69-74,共6页微分方程年刊（英文版）

基　　金：Supported by NSFC (10171032).

摘　　要：In this paper, when μ 〈 1/4, and 2 〈 q 〈 2（3- σ）,0 ≤ σ ≤ 2 we discuss the existence of the solution for a nonlinear elliptic equation by an improved Sobolev-Hardy inequality. We also proved that the constant is optimal in the improved Sobolev-Hardy inequality. We also prove that the problem has no nontrivial solution when │y│ 〈 R, μ 〉 0 and q = 2（3- σ）, the method is coming from the idea of Pohozaev.In this paper, when μ 〈 1/4, and 2 〈 q 〈 2（3- σ）,0 ≤ σ ≤ 2 we discuss the existence of the solution for a nonlinear elliptic equation by an improved Sobolev-Hardy inequality. We also proved that the constant is optimal in the improved Sobolev-Hardy inequality. We also prove that the problem has no nontrivial solution when │y│ 〈 R, μ 〉 0 and q = 2（3- σ）, the method is coming from the idea of Pohozaev.

关 键 词：elliptic equation Sobolev-Hardy inequality critical singularity Mountain Pass Theorem 

分 类 号：O175.25[理学—数学]