一类具有转移条件的Sturm-Liouville方程的谱性质

摘要/Abstract

摘要：

研究一类具有转移条件和特征参数相关边界条件的不连续的Sturm-Liouville方程.构造了一个新的算子,并且在新的Hilbert空间中证明了其自伴性.构造了基本解,给出了特征值和特征函数的一些性质,以及渐近估计式,证明了特征函数系的完备性,并且得到了问题的格林函数和预解算子.

关键词: 转移条件, 权函数, 特征参数相关边界条件, 特征值和特征函数的估计式, 特征函数完备性, 格林函数, 预解算子

Abstract:

In this paper, a discontinuous Sturm-Liouville equation with eigenparameter-dependent boundary conditions and transmission conditions is considered. A new operator associated with the problem is constructed, the self-adjointness of the operator in an appropriate Hilbert space is proved, the fundamental solutions are constructed, some properties of the eigenvalues and corresponding eigenfunctions are investigated, the asymptotic formulas for the eigenvalues and eigenfunctions are given, the completeness of eigenfunctions, Green function and the resolvent operator are also involved.

Key words: Transmission conditions, Weight function, Eigenparameter-dependent boundary condition, The asymptotic formulas of eigenvalues and eigenfunctions, Completeness, Green function, Resolvent operator

中图分类号:

O175.1

李昆, 郑召文. 一类具有转移条件的Sturm-Liouville方程的谱性质[J]. 数学物理学报, 2015, 35(5): 910-926.

Li Kun, Zheng Zhaowen. Spectral Properties for Sturm-Liouville Equations with Transmission Conditions[J]. Acta mathematica scientia,Series A, 2015, 35(5): 910-926.

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