Abstract
We prove the existence of positive continuous solutions to the nonlinear fractional problem
(-Delta(vertical bar D))(alpha/2) u + lambda f(., u) = 0,
in a bounded C-1,C-1-domain D in R-n (n >= 2), subject to some Dirichlet conditions, where 0 < alpha < 2 and lambda is a positive number. The function f is nonnegative continuous monotone with respect to the second variable and satisfying some adequate hypotheses related to the Kato class. Our approach is based on Schauder's fixed point Theorem.