The Brezis–Nirenberg Problem for the Fractional p-Laplacian in Unbounded Domains

In this paper we study the existence of nontrivial solutions to the well-known Brezis–Nirenberg problem involving the fractional p-Laplace operator in unbounded cylinder type domains.By means of the fractional Poincaré inequality in unbounded cylindrical domains, we first study the asymptotic property of the first eigenvalue λp,s(■) with respect to the domain■. Then, by applying the concentration-compactness principle for fractional Sobolev spaces in unbounded domains, we prove the existence res...