Abstract
The purpose of the present paper is to study the existence of solutions for the following nonhomogeneous singular problem involving the fractional
-Laplace operator
where Ω is a smooth bounded domain in
(
),
, λ is a positive parameter and
is a continuous function,
is a bounded, continuous and symmetric function,
is a continuous function,
and
with
. Here, the nonlinearity f is in
and assumed to satisfy suitable assumptions. Using variational methods combined with monotonicity arguments, we obtain the existence of solutions to the problem in a fractional Sobolev space with variable exponent. To our best knowledge, this paper is the first attempt in the study of singular problems involving fractional
-Laplace operators.