Positive solutions for some competitive fractional systems in bounded domains
Summary: 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 \((-\Delta_{|D})^{\alpha/2}u + p(x)u^\sigma v^r = 0\), \((-\Delta_{|D})^{\alpha/2}v + q(x)u^sv^\beta = 0\) in a bounded \(C^{1,1}\)-domain \(D\) in \(\mathbb R^n(n \geq 3)\), subject to some Dirichlet conditions, where \(0 < \alpha < 2, \sigma, \beta \geq 1, s, r \geq 0\). The potential functions \(p, q\) are nonnegative and required to satisfy some adequate hypotheses related to the Kato class of functions \(K_\alpha(D)\).
scientific article; zbMATH DE number 6167891