An eigenvalue result for Neumann BVPs with functional terms
Classical Analysis and ODEs
2026-04-15 v1 Numerical Analysis
Numerical Analysis
Abstract
We study the existence and localization of eigenvalue-eigenfunction pairs for parameter-dependent Neumann BVPs with a functional term. By reformulating the problems as a Hammerstein integral equation, we apply an existence and localization result and propose a convergent fixed-point iteration scheme. Finally, two pseudocodes and a MATLAB implementation are provided to numerically approximate the eigenvalues and validate the theoretical localization bounds. We also illustrate an approximation of the eigenfunctions for a fixed norm.
Cite
@article{arxiv.2604.12415,
title = {An eigenvalue result for Neumann BVPs with functional terms},
author = {Giuseppe Antonio Veltri},
journal= {arXiv preprint arXiv:2604.12415},
year = {2026}
}
Comments
19 pages, 5 figures