On the solvability of parameter-dependent elliptic functional BVPs on annular-like domains

TL;DR

This paper studies the existence of solutions for parameter-dependent elliptic boundary value problems with functional boundary conditions in annular-like domains, using topological methods and an example to demonstrate applicability.

Contribution

It introduces a new existence result for elliptic BVPs with deviated arguments in annular domains using a variant of the Birkhoff--Kellogg theorem.

Findings

Existence of nontrivial solutions established

Application of topological methods in elliptic BVPs

Illustrative example demonstrating theoretical results

Abstract

We investigate the existence of nontrivial solutions of parameter-dependent elliptic equations with deviated argument in annular-like domains in $\mathbb{R}^{n}$, with $n\geq 2$, subject to functional boundary conditions. In particular we consider a boundary value problem that may be used to model heat-flow problems. We obtain an existence result by means of topological methods; in particular, we make use of a recent variant in affine cones of the celebrated Birkhoff--Kellogg theorem. Using an ODE argument, we illustrate in an example the applicability of our theoretical result.