Abstract
We consider the fractional critical problem A(s)u = K(x)u((n+2s)/(n 2s)), u > 0 in Omega, u = 0 on partial derivative Omega, where A(s), s is an element of (0, 1), is the fractional Laplace operator and K is a given function on a bounded domain Omega of R-n, n >= 2. This is based on A. Bahri's theory of critical points at infinity in Bahri [Critical Points at Infinity in Some Variational Problems, Pitman Research Notes in Mathematics Series, 182 (Longman Scientific & Technical, Harlow, 1989)]. We prove Bahri's estimates in the fractional setting and we provide existence theorems for the problem when K is close to 1.