Inverse spectral problem for differential pencils with a frozen argument

This paper deals with differential pencils possessing a term depending on the unknown function with a fixed argument. We deduce the so called main equation together with its fine structure for the spectral problem. Then, according to the boundary conditions and the position of argument, we describe...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2024-04
Main Authors: Yi-teng, Hu, Sat, Murat
Format: Article
Language:English
Subjects:
Boundary conditions
Fine structure
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:This paper deals with differential pencils possessing a term depending on the unknown function with a fixed argument. We deduce the so called main equation together with its fine structure for the spectral problem. Then, according to the boundary conditions and the position of argument, we describe two cases: degenerate and non-degenerate. For these two cases, the uniqueness of inverse spectral problem are studied and a constructive procedure for reconstructing the potentials along with necessary and sufficient conditions of its solvability are obtained.
ISSN:2331-8422