Multiplicity of positive solutions to a critical fractional equation with Hardy potential and concave–convex nonlinearities

Abstract

The aim of this paper is to study the following fractional critical problem with Hardy potential and concave–convex nonlinearities where is the fractional Laplace operator, , is a smooth bounded domain containing the origin, N>2s, , , with is the fractional critical Sobolev exponent. Under suitable hypotheses on μ and N, we prove the existence of at least two positive solutions for the concave case with for some . Moreover, in the convex power case , we show that there exists at least one positive solution for suitable values of λ depending on the dimension N.