Mathematics

CLC number: O175.3

Inverse Sturm-Liouville Problems with a Class of Non-Self-Adjoint Boundary Conditions Containing the Spectral Parameter

一类具有非自伴谱参数边界条件的 Sturm-Liouville 逆问题

¹ College of Sciences, Inner Mongolia University of Technology, Hohhot 010051, Inner Mongolia, China
² E-Learning Network Center, Ordos Municipal Party Committee School, Ordos 017000, Inner Mongolia, China

^† Corresponding author. E-mail: george_ao78@sohu .com

Received: 18 February 2024

Abstract

The inverse spectral theory of a class of Atkinson-type Sturm-Liouville problems with non-self-adjoint boundary conditions containing the spectral parameter is investigated. Based on the so-called matrix representations of such problems and a special class of inverse matrix eigenvalue problems, some of the coefficient functions of the corresponding Sturm-Liouville problems are constructed by using priori known two sets of complex numbers satisfying certain conditions. To best understand the result, an algorithm and some examples are posted.

摘要

本文研究一类具有非自伴谱参数边界条件的Atkinson类型Sturm-Liouville逆谱问题。利用此类问题的矩阵表示，并基于一类特殊的矩阵逆特征值问题，通过应用已知的两组满足一定条件的复数构造出此类Sturm-Liouville问题的一些系数函数。为了更好地理解主要结论，我们给出了对应算法和一些示例。