Fractional Hardy-Sobolev operator with sign-changing and singular nonlinearity

Abstract

We study the following fractional equation with Hardy potential and singular nonlinearity where is a bounded domain in with smooth boundary , n>2s, , the sharp constant of the fractional Hardy Sobolev inequality, , with , such that , and is a sign-changing function such that . Using variational methods, we show existence, non-existence and multiplicity of positive solutions of with respect to the parameter λ.