Existence of multiple solutions for a quasilinear Neumann problem with critical exponent

Abstract

Abstract The main purpose of this paper is to establish the existence and multiplicity of nontrivial solutions for a quasilinear Neumann problem with critical exponent. It is shown, by the methods of the Lions concentration-compactness principle and the mountain pass lemma, that under certain conditions, the existence of nontrivial solutions are obtained.

Keywords

• Quasilinear elliptic equation
• Nontrivial solution
• Neumann boundary condition
• Critical Sobolev exponent
• Lions concentration-compactness principle