A Singular Sturm-Liouville Problem with Limit Circle Endpoints and Eigenparameter Dependent Boundary Conditions

A Singular Sturm-Liouville Problem with Limit Circle Endpoints and Eigenparameter Dependent Boundary Conditions

In this paper, we investigate a class of discontinuous singular Sturm-Liouville problems with limit circle endpoints and eigenparameter dependent boundary conditions. Operator formulation is constructed and asymptotic formulas for eigenvalues and fundamental solutions are given. Moreover, the comple...

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Main Authors: Jinming Cai, Zhaowen Zheng
Format: Article
Language:English
Published: Hindawi Limited 2017-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2017/9673846
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spelling doaj-80c11180fdbd4f979ce2ee7255e5af642020-11-24T22:37:55ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2017-01-01201710.1155/2017/96738469673846A Singular Sturm-Liouville Problem with Limit Circle Endpoints and Eigenparameter Dependent Boundary ConditionsJinming Cai0Zhaowen Zheng1School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong 273165, ChinaSchool of Mathematical Sciences, Qufu Normal University, Qufu, Shandong 273165, ChinaIn this paper, we investigate a class of discontinuous singular Sturm-Liouville problems with limit circle endpoints and eigenparameter dependent boundary conditions. Operator formulation is constructed and asymptotic formulas for eigenvalues and fundamental solutions are given. Moreover, the completeness of eigenfunctions is discussed.http://dx.doi.org/10.1155/2017/9673846
collection DOAJ
language English
format Article
sources DOAJ
author Jinming Cai
Zhaowen Zheng
spellingShingle Jinming Cai
Zhaowen Zheng
A Singular Sturm-Liouville Problem with Limit Circle Endpoints and Eigenparameter Dependent Boundary Conditions
Discrete Dynamics in Nature and Society
author_facet Jinming Cai
Zhaowen Zheng
author_sort Jinming Cai
title A Singular Sturm-Liouville Problem with Limit Circle Endpoints and Eigenparameter Dependent Boundary Conditions
title_short A Singular Sturm-Liouville Problem with Limit Circle Endpoints and Eigenparameter Dependent Boundary Conditions
title_full A Singular Sturm-Liouville Problem with Limit Circle Endpoints and Eigenparameter Dependent Boundary Conditions
title_fullStr A Singular Sturm-Liouville Problem with Limit Circle Endpoints and Eigenparameter Dependent Boundary Conditions
title_full_unstemmed A Singular Sturm-Liouville Problem with Limit Circle Endpoints and Eigenparameter Dependent Boundary Conditions
title_sort singular sturm-liouville problem with limit circle endpoints and eigenparameter dependent boundary conditions
publisher Hindawi Limited
series Discrete Dynamics in Nature and Society
issn 1026-0226
1607-887X
publishDate 2017-01-01
description In this paper, we investigate a class of discontinuous singular Sturm-Liouville problems with limit circle endpoints and eigenparameter dependent boundary conditions. Operator formulation is constructed and asymptotic formulas for eigenvalues and fundamental solutions are given. Moreover, the completeness of eigenfunctions is discussed.
url http://dx.doi.org/10.1155/2017/9673846
work_keys_str_mv AT jinmingcai asingularsturmliouvilleproblemwithlimitcircleendpointsandeigenparameterdependentboundaryconditions
AT zhaowenzheng asingularsturmliouvilleproblemwithlimitcircleendpointsandeigenparameterdependentboundaryconditions
AT jinmingcai singularsturmliouvilleproblemwithlimitcircleendpointsandeigenparameterdependentboundaryconditions
AT zhaowenzheng singularsturmliouvilleproblemwithlimitcircleendpointsandeigenparameterdependentboundaryconditions
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