Positive Solutions for Some Competitive Fractional Systems in Bounded Domains

Using some potential theory tools and the Schauder fixed point theorem, we prove the existence and precise global behavior of positive continuous solutions for the competitive fractional system (-Delta(vertical bar D))(alpha/2)u + p(x)u(sigma)v(r) = 0, (-Delta(vertical bar D))(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 some 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 of functions K-alpha(D).