A priori bounds and positive solutions for non-variational fractional   elliptic systems
  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
math.AP