Principal curves to fractional m-Laplacian systems and related maximum and comparison principles

In this paper we develop a comprehensive study on principal eigenvalues and both the (weak and strong) maximum and comparison principles related to an important class of nonlinear systems involving fractional m -Laplacian operators. Explicit lower bounds for principal eigenvalues of this system in terms of the diameter of bounded domain Ω ⊂ R N are also proved. As application, we measure explicitly how small has to be diam ( Ω ) so that weak and strong maximum principles associated to this problem hold in Ω .