Existence and Multiplicity Results for Elliptic Equations with Critical Sobolev Exponent and Hardy Term

Abstract

This paper concerns the existence and multiplicity of solutions for some semilinear elliptic equations with critical Sobolev exponent, Hardy term and the sublinear nonlinearity at origin. By using Ekeland's variational principle, we conclude the existence of nontrivial solution for this problem, the Clark's critical point theorem is used to prove the existence of infinitely many solutions for this problem with odd nonlinearity.