Multiple solutions for elliptic problem in $\mathbb{R}^N$ with critical Sobolev exponent and weight function

Abstract

In this paper, existence and multiplicity results for semilinear elliptic equations in whole space, with concave and convex nonlinearities and weight function which can change sign, are established. The study is based on variational methods, more precisely, minimization techniques and mountain pass Theorem without Palais-Smale condition.