Abstract
Using some potential theory tools and the Schauder fixed point theorem, we prove the existence of a positive continuous weak solution for the fractional system
(-Delta)(alpha/2)u + p(x)u(alpha)v(r) = 0, (-Delta)(alpha/2)v + q(x)u(s)v(beta) = 0
in a bounded C-1,C-1-domain D in R-n (n >= 3), subject to Dirichlet conditions, where 0 < alpha < 2, sigma, beta >= 1, s, r >= 0. The potential functions p, q are nonnegative and required to satisfy some adequate hypotheses related to the Kato class K-alpha(D). We also investigate the global behavior of such solution.