Abstract
In this paper we investigate the following nonlocal problem with singular term and critical Hardy-Sobolev exponent
where Ω ⊂ ℝ
is an open bounded domain with Lipschitz boundary, 0 <
< 1, λ > 0 is a parameter, 0 <
< 2
<
, 0 <
< 1 < 2 <
, where
are the fractional critical Sobolev and Hardy Sobolev exponents respectively. The fractional Laplacian (–Δ)
with
∈ (0, 1) is the nonlinear nonlocal operator defined on smooth functions by
By combining variational and approximation methods, we provide the existence of two positive solutions to the problem (P).