Borg-type theorem for a class of fourth-order differential operators

Ai-Wei Guan; Chuan-Fu Yang; Natalia P. Bondarenko

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arXiv · 2412.07413

Borg-type theorem for a class of fourth-order differential operators

Ai-Wei Guan·Chuan-Fu Yang·Natalia P. Bondarenko

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Abstract

In this paper, we study an inverse spectral problem for the fourth-order differential equation $y^{(4)} - (p y')' + q y = \lambda y$ with real-valued coefficients $p$ and $q$ of $L^2(0,1)$. We prove that, for near-constant coefficients, the two spectra corresponding to the Dirichlet and the Dirichlet-Neumann boundary conditions uniquely determine either $p$ or $q$. The result extends the Borg theorem of the second-order case to the fourth-order case.

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BibTeX RIS

Ai-Wei Guan, Chuan-Fu Yang, Natalia P. Bondarenko. 2024-12-10. Borg-type theorem for a class of fourth-order differential operators. https://arxiv.org/abs/2412.07413

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