On the Jost Solutions of A Class of the Quadratic Pencil of the Sturm-Liouville Equation
Süleyman Demirel Üniversitesi Fen Edebiyat Fakültesi Fen Dergisi, vol.18, no.1, pp.18-27, 2023 (TRDizin)
- Publication Type: Article / Article
- Volume: 18 Issue: 1
- Publication Date: 2023
- Doi Number: 10.29233/sdufeffd.1266502
- Journal Name: Süleyman Demirel Üniversitesi Fen Edebiyat Fakültesi Fen Dergisi
- Journal Indexes: Academic Search Premier, CAB Abstracts, Veterinary Science Database, zbMATH, Directory of Open Access Journals, TR DİZİN (ULAKBİM)
- Page Numbers: pp.18-27
- Süleyman Demirel University Affiliated: Yes
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.