An eigenvalue result for Hammerstein integral equations with sign changing nonlinearities and functional terms
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911040809205760 |
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| author | Infante, Gennaro Veltri, Giuseppe Antonio |
| author_facet | Infante, Gennaro Veltri, Giuseppe Antonio |
| contents | We discuss, via a version of the Birkhoff-Kellogg theorem, the existence of positive and negative eigenvalues of Hammerstein integral equations with sign-changing nonlinearities and functional terms. The corresponding eigenfunctions have a given norm that, in turn, provides a location for the eigenvalues. As an application, we study the solvability of parameter-dependent boundary value problems for nonlocal ordinary differential equations. Two examples illustrate the applicability of the theory in the case of mixed and Dirichlet boundary conditions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_15382 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An eigenvalue result for Hammerstein integral equations with sign changing nonlinearities and functional terms Infante, Gennaro Veltri, Giuseppe Antonio Classical Analysis and ODEs Primary 45C05, secondary 34B08, 47H10 We discuss, via a version of the Birkhoff-Kellogg theorem, the existence of positive and negative eigenvalues of Hammerstein integral equations with sign-changing nonlinearities and functional terms. The corresponding eigenfunctions have a given norm that, in turn, provides a location for the eigenvalues. As an application, we study the solvability of parameter-dependent boundary value problems for nonlocal ordinary differential equations. Two examples illustrate the applicability of the theory in the case of mixed and Dirichlet boundary conditions. |
| title | An eigenvalue result for Hammerstein integral equations with sign changing nonlinearities and functional terms |
| topic | Classical Analysis and ODEs Primary 45C05, secondary 34B08, 47H10 |
| url | https://arxiv.org/abs/2505.15382 |