Multiple positive solutions for a critical elliptic problem with concave and convex nonlinearities

Abstract

In this article, we study the multiplicity of positive solutions for a semi-linear elliptic problem involving critical Sobolev exponent and concave-convex nonlinearities. With the help of Nehari manifold and Ljusternik-Schnirelmann category, we prove that problem admits at least cat$(\Omega)+1$ positive solutions.

Keywords

• Nehari manifold
• critical Sobolev exponent
• positive solution
• semi-linear elliptic problem
• Ljusternik-Schnirelmann category