EIGENFUNCTION EXPANSION FOR STURM-LIOUVILLE PROBLEMS WITH TRANSMISSION CONDITIONS AT ONE INTERIOR POINT

doi:10.1016/S0252-9602(15)30010-2

Abstract

Abstract:

The purpose of this article is to extend some spectral properties of regular Sturm-Liouville problems to the special type discontinuous boundary-value problem, which consists of a Sturm-Liouville equation together with eigenparameter-dependent boundary conditions and two supplementary transmission conditions. We construct the resolvent operator and Green's function and prove theorems about expansions in terms of eigenfunctions in modified Hilbert space L₂[a, b].

Key words: Boundary-value problems, transmission conditions, resolvent operator

CLC Number:

34L10

Oktay Sh. MUKHTAROV, Kadriye AYDEMIR. EIGENFUNCTION EXPANSION FOR STURM-LIOUVILLE PROBLEMS WITH TRANSMISSION CONDITIONS AT ONE INTERIOR POINT[J].Acta mathematica scientia,Series B, 2015, 35(3): 639-649.

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