EXISTENCE RESULTS FOR FRACTIONAL BREZIS-NIRENBERG TYPE PROBLEMS IN UNBOUNDED DOMAINS

In this paper we study the fractional Brezis-Nirenberg type problems in unbounded cylinder-type domains {(-Delta)(s)u - mu u/vertical bar x vertical bar 2s - lambda u + vertical bar u vertical bar(2s)* (- 2u) in Omega, u = 0 in R-N\Omega, where (-Delta)(s) is the fractional Laplace operator with s is an element of (0, 1), mu is an element of [0, Lambda(N,s)) with Lambda(N,s) the best fractional Hardy constant, lambda > 0, N > 2s and 2(s)* = 2N/(N - 2s) denotes the fractional critical Sobolev exponent. By applying the fractional Poincare inequality together with the concentration-compactness principle for fractional Sobolev spaces in unbounded domains, we prove an existence result to the equation.