不定型Sturm-Liouville逆问题

傅守忠;徐宗本;魏广生;

数学学报 ›› 2009 ›› Issue (01) : 49-62.

中国科学院数学与系统科学研究院期刊网
数学学报 ›› 2009 ›› Issue (01) : 49-62. DOI: 10.12386/A2009sxxb0005
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不定型Sturm-Liouville逆问题

    傅守忠;徐宗本;魏广生;
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Inverse Sturm-Liouville Problems with Indefined Weighted Functions

    Shou Zhong FU School of Science,Xi'an Jiaotong University,Xi'an 710049,P.R.China Department of Computer Science,Zhaoqing University,Zhaoqing 526061,P.R.China Zong Ben XU Guang Sheng WEI School of Science,Xi'an Jiaotong University,Xi'an 710049,P.R.China
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摘要

讨论权函数是具有一个转点的不定弦方程问题.首先借助Liouville变换将其化归为权函数为分段常函数的不定Sturm-Liouville问题;然后对这类问题的逆问题进行研究,给出对应于权函数为负部分的势函数已知时,唯一确定整个势函数的一些充分条件.

Abstract

We discuss undefined string equation problems where the weighted function is of one turning-point.Firstly,making use of Liouville transformation,we transform it into undefined Sturm-Liouville Problems where its weighted function is a piecewise constant function.Then we study the undefined Sturm-Liouville inverse eigenvalue problems,and give some sufficient conditions for the corresponding potential functions are determined uniquely,when the negative part of potential functions is given.

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特征值 / Sturm-Liouville算子 / 逆问题

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eigenvalue inverse problem / Sturm-Liouville operator

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傅守忠;徐宗本;魏广生;. 不定型Sturm-Liouville逆问题. 数学学报, 2009(01): 49-62 https://doi.org/10.12386/A2009sxxb0005
Shou Zhong FU School of Science,Xi'an Jiaotong University,Xi'an 710049,P.R.China Department of Computer Science,Zhaoqing University,Zhaoqing 526061,P.R.China Zong Ben XU Guang Sheng WEI School of Science,Xi'an Jiaotong University,Xi'an 710049,P.R.China. Inverse Sturm-Liouville Problems with Indefined Weighted Functions. Acta Mathematica Sinica, Chinese Series, 2009(01): 49-62 https://doi.org/10.12386/A2009sxxb0005

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