Nonzero positive solutions of fractional Laplacian systems with functional terms

Abstract

We study the existence of non-zero positive solutions of a class of systems of differential equations driven by fractional powers of the Laplacian.Our approach is based on the notion of fixed point index, and allows us to deal with non-local functional weights and functional boundary conditions.We present two examples to shed light on the type of functionals and growth conditions that can be considered with our approach.