Article Contents

2024, Volume 17, Issue 5&6: 2009-2020. Doi: 10.3934/dcdss.2023006

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On fourth order retarded equations with functional boundary conditions: A unified approach

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

Dedicated to Professor Jerome A. Goldstein in honor of his eightieth birthday

Received: September 2022

Revised: December 2022

Early access: January 2023

Published: May 2024

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Abstract

By means of a recent Birkhoff-Kellogg type theorem, we discuss the solvability of a fairly general class of parameter-dependent fourth order retarded differential equations subject to functional boundary conditions. We seek solutions within a translate cone of nonnegative functions. We provide an example to illustrate our theoretical results.

Keywords:

Fixed point index,
cone,
Birkhoff–Kellogg type result,
retarded functional differential equation,
functional boundary condition.

Mathematics Subject Classification: Primary: 47H10; Secondary: 34K10, 34B10, 34B18.

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References

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