具有不连续系数且边界条件下含有特征参数的Sturm-Liouville问题

Physics Research International Pub Date : 2012-12-12 DOI:10.1155/2013/159243

E. Şen

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引用次数: 1

摘要

研究了具有特征参数依赖边界条件和内部两点传输条件的Sturm-Liouville算子。给出了不连续Sturm-Liouville问题的算子理论表述，构造了基本解，研究了不连续Sturm-Liouville问题的特征值和特征函数的一些性质，得到了不连续Sturm-Liouville问题的特征值和特征函数的渐近公式，并求出了该问题的Green函数。

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A Sturm-Liouville Problem with a Discontinuous Coefficient and Containing an Eigenparameter in the Boundary Condition

We study a Sturm-Liouville operator with eigenparameter-dependent boundary conditions and transmission conditions at two interior points. We give an operator-theoretic formulation, construct fundamental solutions, investigate some properties of the eigenvalues and corresponding eigenfunctions of the discontinuous Sturm-Liouville problem and then obtain asymptotic formulas for the eigenvalues and eigenfunctions and find Green function of the discontinuous Sturm-Liouville problem.

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Physics Research International

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