SINGULAR CRITICAL ELLIPTIC PROBLEMS WITH FRACTIONAL LAPLACIAN

In this article, we consider the existence of solutions of the critical problem with a Hardy term for fractional Laplacian (-Delta)(s)u - mu u/vertical bar x vertical bar(2s) = u(2)*s(-1) in Omega, u > 0 in Omega, u = 0 on partial derivative Omega, where Omega subset of R-N is a smooth bounded domain and 0 is an element of Omega, mu is a positive parameter, N > 2s and s is an element of (0, 1), 2*(s) = 2N/N-2s is the critical exponent. (-Delta)(s) stands for the spectral fractional Laplacian. Assuming that Omega is non-contractible, we show that there exists mu(0) > 0 such that 0 < mu < mu(0), there exists a solution. We also discuss a similar problem for the restricted fractional Laplacian.