Electron. J. Diff. Equ., Vol. 2016 (2016), No. 12, pp. 1-8.

Semilinear elliptic problems involving Hardy-Sobolev-Maz'ya potential and Hardy-Sobolev critical exponents

Rui-Ting Jiang, Chun-Lei Tang

Abstract:
In this article, we study a class of semilinear elliptic equations involving Hardy-Sobolev critical exponents and Hardy-Sobolev-Maz'ya potential in a bounded domain. We obtain the existence of positive solutions using the Mountain Pass Lemma.

Submitted July 14, 2015. Published January 7, 2016.
Math Subject Classifications: 35B09, 35B33, 35J75.
Key Words: Hardy-Sobolev-Maz'ya potential; Hardy-Sobolev critical exponents; positive solution; Mountain Pass Lemma; local Palais-Smale condition.

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Rui-Ting Jiang
School of Mathematics and Statistics
Southwest University
Chongqing 400715, China
email: 1152373321@qq.com
Chun-Lei Tang
School of Mathematics and Statistics
Southwest University
Chongqing 400715, China
phone +86 23 68253135, fax +86 23 68253135
email: tangcl@swu.edu.cn

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