Nehari manifold for singular fractional p(x,.)-Laplacian problem

In this paper, we consider a class of fractional Laplacian problems of the form: {(-Delta)(p(x,.))(s) u+mu vertical bar u vertical bar(q(x)-2)u=lambda g(x)u(-gamma(x) )+ f(x, u) in Omega, u = 0, on partial derivative Omega, where Omega subset of R-N, (N >= 2), is a bounded domain and (-Delta)(p)(s)((x,.)()) is the fractional p(x,.)-Laplacian operator. We assume that lambda and mu are positive parameters and gamma : (Omega) over bar -> (0, 1) is a continuous function. By opting for the Nehari manifold method combined with the theory of generalized Lebesgue Sobolev spaces, we will prove the existence of solutions to the above problem.