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.
2010 Mathematics Subject Classifications:
Disclosure statement
No potential conflict of interest was reported by the author(s).