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

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

数学物理学报(英文版) ›› 2015, Vol. 35 ›› Issue (3): 639-649.doi: 10.1016/S0252-9602(15)30010-2

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

Oktay Sh. MUKHTAROV^1,2, Kadriye AYDEMIR²

1. Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences, Baku, Azerbaijan;
2. Department of Mathematics, Faculty of Science, Gaziosmanpasa University, 60250 Tokat, Turkey

收稿日期:2014-01-06 出版日期:2015-05-01 发布日期:2015-05-01

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

Oktay Sh. MUKHTAROV^1,2, Kadriye AYDEMIR²

1. Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences, Baku, Azerbaijan;
2. Department of Mathematics, Faculty of Science, Gaziosmanpasa University, 60250 Tokat, Turkey

Received:2014-01-06 Online:2015-05-01 Published:2015-05-01

摘要/Abstract

摘要：

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].

关键词: Boundary-value problems, transmission conditions, resolvent operator

Abstract:

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

中图分类号:

34L10

Oktay Sh. MUKHTAROV, Kadriye AYDEMIR. EIGENFUNCTION EXPANSION FOR STURM-LIOUVILLE PROBLEMS WITH TRANSMISSION CONDITIONS AT ONE INTERIOR POINT[J]. 数学物理学报(英文版), 2015, 35(3): 639-649.

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

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

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