Abstract
We prove the existence of positive continuous solutions to the nonlinear fractional system
(-Delta vertical bar(D))(alpha/2)u + lambda g(.,v) = 0,
(-Delta vertical bar(D))(alpha/2)v + mu f(.,u) = 0,
in a bounded C-1,C-1-domain D in R-n (n >= 3), subject to Dirichlet conditions, where 0 < alpha <= 2, lambda and mu are nonnegative parameters. The functions f and g are nonnegative continuous monotone with respect to the second variable and satisfying certain hypotheses related to the Kato class.