An eigenvalue result for Neumann BVPs with functional terms
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914471099760640 |
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| author | Veltri, Giuseppe Antonio |
| author_facet | Veltri, Giuseppe Antonio |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_12415 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An eigenvalue result for Neumann BVPs with functional terms Veltri, Giuseppe Antonio Classical Analysis and ODEs Numerical Analysis 34B08 (Primary), 45C05, 65L10 (Secondary) 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. |
| title | An eigenvalue result for Neumann BVPs with functional terms |
| topic | Classical Analysis and ODEs Numerical Analysis 34B08 (Primary), 45C05, 65L10 (Secondary) |
| url | https://arxiv.org/abs/2604.12415 |