Abstract
Let D be a bounded C-1,C-1-domain in R-n (n >= 2) and 0 < alpha < 2. We prove the existence and global asymptotic behavior of positive continuous solutions to the following nonlinear fractional problem (-Delta(vertical bar D))(alpha/2) u = f (.,u) in D, subject to some boundary conditions. In particular, we obtain solutions which blow-up at the boundary. Here, the nonlinearity f is required to satisfy some appropriate conditions related to a Kato class K-alpha (D). Our approach is based on the Schauder's fixed point theorem.