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arXiv · 2412.20985

Eigenvalues of a third order BVP subject to functional BCs

Gennaro Infante·Paolo Lucisano
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Abstract

We discuss the existence of eigenvalues for a third order boundary value problem subject to functional boundary conditions and higher order derivative dependence in the nonlinearities. We prove the existence of positive and negative eigenvalues and provide a localization of the corresponding eigenfunctions in terms of their norm. The methodology involves a version of the classical Birkhoff-Kellogg theorem. We illustrate the applicability of the theoretical results in an example.

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Gennaro Infante, Paolo Lucisano. 2024-12-30. Eigenvalues of a third order BVP subject to functional BCs. https://doi.org/10.12775/tmna.2025.041

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