求解一类不连续的Sturm-Liouville问题

王桂霞;孙炯

系统科学与数学 ›› 2009, Vol. 29 ›› Issue (6) : 839-848.

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系统科学与数学 ›› 2009, Vol. 29 ›› Issue (6) : 839-848. DOI: 10.12341/jssms08423
论文

求解一类不连续的Sturm-Liouville问题

    王桂霞(1), 孙炯(2)
作者信息 +

Solving a Class of Discontinuous Sturm-Liouville Problems

    WANG Guixia(1), SUN Jiong(2)
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文章历史 +

摘要

研究一类边界条件中有谱参数的不连续的Sturm-Liouville问题. 首先在Hilbert空间中定义了一个自共轭的线性算子A,使得该类Sturm-Liouville 问题的特征值与算子A的特征值相一致.
进一步证明了算子A是自共轭的, 且这类Sturm-Liouville问题特征值是解析单的.最后展示了一个具体问题的特征值以及特征函数的逼近解.

Abstract

In this paper, a class of discontinuous Sturm-Liouville problems with eigenparameter dependent boundary conditions is considered. A self-adjoint linear operator A associated with the system is defined in a suitable Hilbert space. It is proven that the eigenvalues of the problem are analytically simple. Accordingly, some approximate solutions of eigenvalues and eigenfunctions are given.

关键词

不连续的Sturm-Liouville 问题 / 谱参数依赖 / 特征值 / 解析单 / 逼近解.

Key words

Discontinuous Sturm-Liouville problems / eigenparameter dependent / eigenvalue / analytically simple / approximate solutions.

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王桂霞 , 孙炯. 求解一类不连续的Sturm-Liouville问题. 系统科学与数学, 2009, 29(6): 839-848. https://doi.org/10.12341/jssms08423
WANG Guixia , SUN Jiong. Solving a Class of Discontinuous Sturm-Liouville Problems. Journal of Systems Science and Mathematical Sciences, 2009, 29(6): 839-848 https://doi.org/10.12341/jssms08423
中图分类号: 34B24    65L10   
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