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

Authors : Zeynep DURNA, Ahmet Sinan ÖZKAN

Pages : 720-730

Doi:10.31801/cfsuasmas.1036073

View : 15 | Download : 7

Publication Date : 2022-09-30

Article Type : Research Paper

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