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

Alessandro Calamai; Gennaro Infante

doi:10.3934/dcdsb.2024193

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2025, Volume 30, Issue 11: 4287-4295. Doi: 10.3934/dcdsb.2024193

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

Alessandro Calamai^1, and
Gennaro Infante^2, ,

1.
Dipartimento di Ingegneria Civile, Edile e Architettura, Università Politecnica delle Marche, Italy
2.
Dipartimento di Matematica e Informatica, Università della Calabria, Italy

^*Corresponding author: Gennaro Infante
^*Corresponding author: Gennaro Infante

Received: October 2024

Revised: December 2024

Early access: January 3, 2025

Published online: January 3, 2025

The authors were partly funded by the Research project of MUR - Prin 2022 “Nonlinear differential problems with applications to real phenomena” [Grant Number: 2022ZXZTN2].

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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.

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Mathematics Subject Classification: Primary: 35J15, Secondary 35B09, 35J25, 35J60, 47H10.

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