Eigenvalues of a coupled system of thermostat-type via a Birkhoff-Kellogg type Theorem
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917006578548736 |
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| author | Ullah, Sajid |
| author_facet | Ullah, Sajid |
| contents | In this paper, by means of Birkhoff--Kellogg type Theorem in cones we address the existence of eigenvalues and the corresponding eigenvectors to a family of coupled system of thermostat type. The system is characterized by the presence of a real parameter that influences not only the differential equations but also the boundary conditions. Motivated by models of temperature regulation and feedback-controlled systems, we reformulate the original boundary value problems into systems of Hammerstein integral equations. The theoretical results are applied to three different classes of boundary conditions in $t=0$, which are supported by examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_08516 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Eigenvalues of a coupled system of thermostat-type via a Birkhoff-Kellogg type Theorem Ullah, Sajid Classical Analysis and ODEs Primary 34B08, secondary 34B10, 47H30 In this paper, by means of Birkhoff--Kellogg type Theorem in cones we address the existence of eigenvalues and the corresponding eigenvectors to a family of coupled system of thermostat type. The system is characterized by the presence of a real parameter that influences not only the differential equations but also the boundary conditions. Motivated by models of temperature regulation and feedback-controlled systems, we reformulate the original boundary value problems into systems of Hammerstein integral equations. The theoretical results are applied to three different classes of boundary conditions in $t=0$, which are supported by examples. |
| title | Eigenvalues of a coupled system of thermostat-type via a Birkhoff-Kellogg type Theorem |
| topic | Classical Analysis and ODEs Primary 34B08, secondary 34B10, 47H30 |
| url | https://arxiv.org/abs/2510.08516 |