In this paper, we study strongly coupled elliptic systems in non-variational form involving fractional Laplace operators. We prove Liouville type theorems and, by mean of the blow-up method, we establish a priori bounds of positive solutions for subcritical and superlinear nonlinearities in a coupled sense. By using those latter, we then derive the existence of positive solutions through topological methods.
Edir Junior Ferreira Leite. Marcos Montenegro. "A priori bounds and positive solutions for non-variational fractional elliptic systems." Differential Integral Equations 30 (11/12) 947 - 974, November/December 2017. https://doi.org/10.57262/die/1504231281