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

Abstract

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 \(\varOmega \subset {\mathbb {R}}^N\) are also proved. As application, we measure explicitly how small has to be \(\text {diam}(\varOmega )\) so that weak and strong maximum principles associated to this problem hold in \(\varOmega \).