About one inverse problem for the Sturm-Liouville operator

2019/12/06 by B. N. Biyarov, Biyarov, B. N.
Mathematics · Computer Science · Materials Science · #Spectral Theory in Mathematical Physics #Advanced Mathematical Modeling in Engineering #Quasicrystal Structures and Properties

paper · pdf · doi:10.48550/arxiv.1912.03129

Abstract

We consider the spectral problems for the Sturm-Liouville operator generated by the Dirichlet, Neumann, Dirichlet-Neumann and Neumann-Dirichlet conditions. The necessary and sufficient condition for the coincidence of the spectrum of the Dirichlet-Neumann and Neumann-Dirichlet problems is proved. Also the necessary and sufficient condition for the coincidence of the spectrum, except zero, of the Dirichlet and Neumann problems is proved. An application to periodic and anti-periodic problems is given.

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