Abstract
In this article we study a nonlocal equation involving singular and critical Hardy-Sob olev non-linearities, (-delta(p))(s)u - mu|u|(p-2)u(sp)/|x| = lambda u(-alpha) + |u|p(s)(& lowast;(t)-2)u/|x|(t) , in omega, u > 0, in omega, u = 0, in R-N \ omega,where omega subset of R-N is a bounded domain with Lipschitz boundary and (-delta(p))(s) is the fractional p-Laplacian operator. We combine some variational techniques with a perturbation method to show the existence of multiple solutions.