An affine Birkhoff-Kellogg type result in product spaces and its application to differential systems
Abstract
We prove a version of the Birkhoff-Kellogg theorem in product spaces, under affine transformations. This is a fairly natural framework that arises when dealing with parameter-dependent systems of functional-differential equations. We provide criteria on the existence of parameter-dependent solutions that have all the components nontrivial. The theoretical results are illustrated in the case of systems of second order functional-differential equations, where the functional part can cover the interesting cases of time and state-dependent deviated arguments. We provide a concrete example, for which we furnish numerically approximated solutions, coherent with our theoretical framework, and in which we compute or estimate all the constants that are required by our abstract results.
Related
- A product inequality and its application to cross-intersecting families
- Why the Kellogg Mesh Is Radial: A Mathematical Explanation of a Classical Computational Benchmark
- Best proximity point results of operator type condensing mappings via measure of noncompactness and application to an infinite system of differential equations in c0 and ℓ1
- On the Luxemburg Functional in the Concave Regime with an Application to Nonlocal Differential Equations
- Differentiability of the Leading Lyapunov Exponent of a linear differential equation with random coefficients Application to the Calculation of the Selection Gradient in Random Environments
BibTeX
@misc{calamai2026affine,
title = {{An affine Birkhoff-Kellogg type result in product spaces and its application to differential systems}},
author = {Alessandro Calamai and Gennaro Infante and Giuseppe Antonio Veltri},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.16909},
eprint = {2607.16909},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.16909},
}
RIS
TY - UNPB
TI - An affine Birkhoff-Kellogg type result in product spaces and its application to differential systems
AU - Alessandro Calamai
AU - Gennaro Infante
AU - Giuseppe Antonio Veltri
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2607.16909
UR - https://arxiv.org/abs/2607.16909
AB - We prove a version of the Birkhoff-Kellogg theorem in product spaces, under affine transformations. This is a fairly natural framework that arises when dealing with parameter-dependent systems of functional-differential equations. We provide criteria on the existence of parameter-dependent solutions that have all the components nontrivial. The theoretical results are illustrated in the case of systems of second order functional-differential equations, where the functional part can cover the interesting cases of time and state-dependent deviated arguments. We provide a concrete example, for which we furnish numerically approximated solutions, coherent with our theoretical framework, and in which we compute or estimate all the constants that are required by our abstract results.
ER -