Eigenvalue problems for a class of Sturm-Liouville operators on two different time scales
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Date
2022
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Ankara Üniversitesi
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:
T
=
[
α
,
δ
1
]
⋃
[
δ
2
,
β
]
.
Description
Keywords
Dynamic equations, time scales, measure chains, eigenvalue problems, Sturm-Liouville theory