Existence of solution for a singular fractional Laplacian problem with variable exponents and indefinite weights

In this paper, we consider a class of fractional Laplacian problems of the form: (−Δ)p1(x,.)su+(−Δ)p2(x,.)su+|u|q(x)−2u=g(x)u−γ(x)+λf(x,u)in Ω,u=0,on ∂Ω, where Ω⊂RN, (N≥2), is a bounded domain and (−Δ)pi(x,.)s is the fractional pi(x,.)-Laplacian. We assume that λ is a nonnegative parameter and γ:Ω¯→(0,1) is a continuous function. By using variational methods and monotonicity arguments combined with the theory of the generalized Lebesgue Sobolev spaces, we prove the existence of solutions to problem (Pλ).