Existence of positive solutions for generalized fractional Brézis-Nirenberg problem

In this article, we study the fractional Brézis-Nirenberg type problem on whole domain N associated with the fractional p-Laplace operator. To be precise, we want to study the following problem: {equation} {Pr1} (-Δₚ)ˢu - λ w |u|ᵖ⁻²u= |u|^{pₛ*-2}u in Ds,p(RN) , {P} {equation} where s∈ (0,1), p∈ (1, N/s), pₛ*=Np/(N-sp) and the operator (-Δₚ)ˢ is the fractional p-Laplace operator. The space Ds,p(RN) is the completion of Cc^∞(N) with respect to the Gagliardo semi-norm. In this article, we prove the existence of a positive solution to problem {Pr1} by allowing the Hardy weight function w to change its sign.