Multiple positive solutions for fractional elliptic systems involving sign-changing weight

Abstract

We study multiplicity results for positive solutions for a fractional elliptic system involving both concave-convex and critical growth terms. With the help of Nehari manifold and Ljusternik-Schnirelmann category, we investigate how the coefficient $h$ of the critical nonlinearity affects the number of positive solutions to this problem and get a relationship between the number of positive solutions and the topology of the global maximum set of $h$.