- Süleyman Demirel Üniversitesi Fen Edebiyat Fakültesi Dergisi
- Vol: 18 Issue: 1
- On the Jost Solutions of A Class of the Quadratic Pencil of the Sturm-Liouville Equation
On the Jost Solutions of A Class of the Quadratic Pencil of the Sturm-Liouville Equation
Authors : Anar Adiloğlu, Döndü Nurten Cücen
Pages : 18-27
Doi:10.29233/sdufeffd.1266502
View : 40 | Download : 58
Publication Date : 2023-05-25
Article Type : Research Article
Abstract :In this study we construct new integral representations of Jost-type solutions of the quadratic pencil of the Sturm-Liouville equation with the piece-wise constant coefficient on the entire real line. Our aim is to express the special solutions of the Sturm-Liouville quadratic pencil in the form of some integral operators which kernels is related with the potential function of the Sturm-Liouville equation. This problem is technically diffucult due to the discontinous coefficient which causes the kernel function to also have a jump discontinuity.Keywords : Sturm-Liouville equation, operator pencil, transformation operator, diferantial equation with discontinuous cofficients, Jost solution