Abstract
Fractional Yamabe-type equations of the form A(s)u = Ku(n+2s/n-2s), u > 0 in Omega, u = 0 on partial derivative Omega, where Omega is a bounded domain of R-n, n >= 2, K is a given function on Omega and A(s), s is an element of (0, 1), is the fractional Laplacian are considered. Bahri's estimates in the fractional setting will be proved and used to establish a global existence result through an index-counting formula.