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In this paper, we consider a class of fractional Laplacian problems of the form:whereis a bounded domain andis the fractional-Laplacian operator. We assume that  λ  and  μ  are positive parameters andis 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.

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