Multiplicity of positive solutions for semilnear elliptic problems with antipodal symmetry

Abstract

In this paper, we show the multiple existence of positive solutions of semilinear elliptic problems of the form $$ -\Delta u=\vert u\vert ^{2^{*}-2}u+f, \quad u\in H_{0}^{1}(\Omega), $$ where $\Omega\subset{\mathbb R}^{N}$ is a bounded domain, $2^{*}$ is the Sobolev critical exponent and $f\in L^{2}(\Omega)$.