# Nontrivial solutions of a parameter-dependent heat flow problem with deviated arguments

## TL;DR

This paper investigates the existence of solutions for a parameter-dependent heat flow problem with deviated arguments using a Birkhoff-Kellogg type theorem in affine cones, providing theoretical insights and a specific example.

## Contribution

It introduces a novel application of a Birkhoff-Kellogg type theorem to analyze solvability of parameter-dependent heat flow problems with deviated arguments.

## Key findings

- Established conditions for the existence of solutions.
- Illustrated the theory with a specific example.
- Identified constants relevant to the solvability criteria.

## Abstract

By means of a recent Birkhoff-Kellogg type theorem set in affine cones, we discuss the solvability of a parameter-dependent thermostat problem subject to deviated arguments. We illustrate in a specific example the constants that occur in our theory.