Solutions for a nonlocal elliptic equation with critical Sobolev exponent and singular term

Abstract

In this paper, we consider a class of nonhomogeneous fractional elliptic equations involving critical Hardy Sobolev exponents as follows {(−Δ)su − μ u |x|2s = |u|2∗ s−2u + λ u |x|2s−α + f(x), x ∈ Ω, u = 0 x ∈ ∂Ω, where Ω ⊂ RN is a bounded domain, 0 < s < 1, λ > 0 is a parameter. We prove the existence of multiple solutions using the variational methods and the Nehari manifold decomposition.