一类具有转移条件的Sturm-Liouville方程的谱性质

Abstract

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

CLC Number:

O175.1

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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Spectral Properties for Sturm-Liouville Equations with Transmission Conditions

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