Nehari manifold for singular fractional<i>p</i>(<i>x</i>,.)-Laplacian problem

Abstract

In this paper, we consider a class of fractional Laplacian problems of the form: {(−Δ)p(x,.)su+μ|u|q(x)−2u=λg(x)u−γ(x)+f(x,u)in Ω,u=0,on ∂Ω, where Ω⊂RN,(N≥2), is a bounded domain and (−Δ)p(x,.)s is the fractional p(x,.)-Laplacian operator. We assume that λ and μ are positive parameters and γ:Ω¯→(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.

Topics & Concepts