Positive Solutions for Some Competitive Fractional Systems in Bounded Domains

Abstract EN

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 (−Δ|D)α/2u+p(x)uσvr=0, (−Δ|D)α/2v+q(x)usvβ=0 in a bounded C1,1-domain D in ℝn (n≥3), subject to some Dirichlet conditions, where 0<α<2, σ,β≥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 Kα(D).