Eigenvalue problems for a class of Sturm-Liouville operators on two different time scales

Year 2022, Volume: 71 Issue: 3, 720 - 730, 30.09.2022

Zeynep Durna Ahmet Sinan Özkan

https://doi.org/10.31801/cfsuasmas.1036073

Abstract

In this study, we consider a boundary value problem generated by the Sturm-Liouville equation with a frozen argument and with non-separated boundary conditions on a time scale. Firstly, we present some solutions and the characteristic function of the problem on an arbitrary bounded time scale. Secondly, we prove some properties of eigenvalues and obtain a formulation for the eigenvalues-number on a finite time scale. Finally, we give an asymptotic formula for eigenvalues of the problem on another special time scale: $\mathbb{T}=[\alpha,\delta_{1}]\bigcup[\delta_{2},\beta].$

Keywords

Dynamic equations , time scales , measure chains , eigenvalue problems , Sturm-Liouville theory

Supporting Institution

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Project Number

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