反斯特姆-刘维尔问题解的重构

IF 1.7 4区数学 Q1 Mathematics

Boundary Value Problems Pub Date : 2024-04-19 DOI:10.1186/s13661-024-01860-4

Zhaoying Wei, Zhijie Hu, Yuewen Xiang

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引用次数: 0

摘要

在本文中，我们关注的是一个具有罗宾边界条件的反问题，即当$[0,1/2]$ 上的势和左端点的系数先验已知时，全谱唯一地决定了其在整个区间上的势和右端点的系数。我们将给出一种新方法，根据与此问题相关的全函数的米塔格-勒弗勒分解来重构此问题的势。新的重构方法还推导出了存在问题的必要条件和充分条件。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Reconstruction of the solution of inverse Sturm–Liouville problem

In this paper we are concerned with an inverse problem with Robin boundary conditions, which states that, when the potential on $[0,1/2]$ and the coefficient at the left end point are known a priori, a full spectrum uniquely determines its potential on the whole interval and the coefficient at the right end point. We shall give a new method for reconstructing the potential for this problem in terms of the Mittag-Leffler decomposition of entire functions associated with this problem. The new reconstructing method also deduces a necessary and sufficient condition for the existence issue.

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来源期刊

Boundary Value Problems MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

3.00

自引率

5.90%

发文量

审稿时长

4 months

期刊介绍： The main aim of Boundary Value Problems is to provide a forum to promote, encourage, and bring together various disciplines which use the theory, methods, and applications of boundary value problems. Boundary Value Problems will publish very high quality research articles on boundary value problems for ordinary, functional, difference, elliptic, parabolic, and hyperbolic differential equations. Articles on singular, free, and ill-posed boundary value problems, and other areas of abstract and concrete analysis are welcome. In addition to regular research articles, Boundary Value Problems will publish review articles.