Multiple positive solutions for a quasilinear elliptic system with critical exponent and sign-changing weight

Abstract

In this paper, our main purpose is to establish the existence of multiple positive solutions of a quasilinear elliptic system with Sobolev critical nonlinearities and sign-changing weight by some standard variational methods. By using the Nehari manifold, fibering maps and the Lusternik–Schnirelmann category, we study the topology of the global maximum set F of f(x), and show the system has at least catFϵ(F)+1 distinct positive solutions, where catFϵ(F) denotes the Lusternik–Schnirelmann category of F in Fϵ.