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

Journal: Süleyman Demirel University Faculty of Arts and Science Journal of Science (Vol.18, No. 1)

Publication Date:

Authors : ; ;

Page : 18-27

Keywords : Sturm-Liouville equation; operator pencil; transformation operator; diferantial equation with discontinuous cofficients; Jost solution;

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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.

Last modified: 2023-09-25 07:07:32