A Study of the scattering analysis of the multiplicative Sturm-Liouville problem


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ÖZNUR G. B., ÖZBEY G. G., Kucukevcilioglu Y. A., Karaman R. A.

TURKISH JOURNAL OF MATHEMATICS, vol.48, no.3, pp.608-622, 2024 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 48 Issue: 3
  • Publication Date: 2024
  • Doi Number: 10.55730/1300-0098.3528
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Page Numbers: pp.608-622
  • Middle East Technical University Affiliated: Yes

Abstract

The main purpose of this study is to examine the scattering analysis of a multiplicative Sturm-Liouville boundary value problem. Firstly, we find the Jost solution of this problem and give the Jost function to construct the scattering function of the problem. Secondly, we obtain asymptotic equations for Jost solution and investigate some properties of the Jost function. Moreover, we present other solutions of the problem by giving the relations between these solutions and Jost solution. Finally, we define the scattering function of this problem by using the Jost function and examine the basic properties of the scattering function.