The Existence of Positive Solution for Semilinear Elliptic Equations with Multiple an Inverse Square Potential and Hardy-Sobolev Critical Exponents

M Khiddi

doi:10.1155/2019/6021293

Abstract

Via the concentration compactness principle, delicate energy estimates, the strong maximum principle, and the Mountain Pass lemma, the existence of positive solutions for a nonlinear PDE with multi-singular inverse square potentials and critical Sobolev-Hardy exponent is proved. This result extends several recent results on the topic.

Highlights

Introduction and Main ResultLet Ω ⊂ RN be smooth open bounded with N > 2
We study the existence of solutions to the following nonlocal problem:
The existence result is obtained via constructing a minimax level within this range and the Mountain Pass Lemma due to A

Summary

Introduction

Introduction and Main ResultLet Ω ⊂ RN be smooth open bounded with N > 2. We study the existence of solutions to the following nonlocal problem: Many important results on the singular problems with Hardy-Sobolev critical exponents

Results

Conclusion