Multiple solutions of a nonlocal system with singular nonlinearities

Abstract

In this work, we study the fractional Laplacian equation with singular nonlinearity: [Formula: see text] where [Formula: see text] is a bounded domain in [Formula: see text] with smooth boundary [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] [Formula: see text] [Formula: see text] is the fractional Sobolev exponent, [Formula: see text] are two parameters, [Formula: see text] are nonnegative weight functions, and [Formula: see text] is the fractional Laplace operator. We use the Nehari manifold approach and some variational techniques in order to show the existence and multiplicity of positive solutions of the above problem with respect to the parameter [Formula: see text] and [Formula: see text].