On the Jost Solutions of A Class of the Quadratic Pencil of the Sturm-Liouville Equation

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Süleyman Demirel Üniversitesi Fen Edebiyat Fakültesi Dergisi
Volume: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 ADİLOĞLU, Döndü Nurten CÜCEN

Pages : 18-27

Doi:10.29233/sdufeffd.1266502

View : 43 | Download : 64

Publication Date : 2023-05-25

Article Type : Research Paper

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

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