Eigenvalues of elliptic functional differential systems via a Birkhoff--Kellogg type theorem

TL;DR

This paper uses a classical nonlinear functional analysis tool to investigate positive eigenvalues in elliptic functional differential systems, motivated by Kirchhoff-type equations, and provides an illustrative example.

Contribution

It introduces a novel application of a Birkhoff--Kellogg type theorem to elliptic functional differential systems for eigenvalue analysis.

Findings

Existence of positive eigenvalues established

Application of Birkhoff--Kellogg theorem demonstrated

Example illustrating the theoretical results provided

Abstract

Motivated by recent interest on Kirchhoff-type equations, in this short note we utilize a classical, yet very powerful, tool of nonlinear functional analysis in order to investigate the existence of positive eigenvalues of systems of elliptic functional differential equations. An example is presented to illustrate the theory.