Nonzero positive solutions of fractional Laplacian systems with functional terms

TL;DR

This paper investigates the existence of positive solutions for fractional Laplacian systems with functional terms, using fixed point index theory to handle non-local weights and boundary conditions.

Contribution

It introduces a fixed point index approach to analyze fractional Laplacian systems with complex functional weights and boundary conditions, expanding the scope of solvable problems.

Findings

Established existence results for positive solutions

Demonstrated applicability with two illustrative examples

Extended methods to non-local and functional boundary conditions

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.