On Nonhomogeneous Elliptic Equations with Critical Sobolev Exponent and Prescribed Singularities

Abstract

In this paper we consider a class of nonhomogeneous elliptic equations involving multi-polar Hardy type potentials and a Sobolev critical nonlinearity in an open domain of $\mathbb{R}^{N}$, $N \geq 3$. By Ekeland's Variational Principle and the Mountain Pass Lemma, we prove the existence of multiple solutions under sufficient conditions on the data and the considered parameters.