Multiplicity of positive solutions for critical singular elliptic systems with sign-changing weight function

Abstract

In this paper, the existence and multiplicity of positive solutions for a critical singular elliptic system with concave and convex nonlinearity and sign-changing weight function, are established. With the help of the Nehari manifold, we prove that the system has at least two positive solutions via variational methods.

Keywords

• critical sobolev exponent
• nehari manifold
• concave-convex nonlinearities
• elliptic system