Non-Self-Adjoint Singular Sturm-Liouville Problems with Boundary Conditions Dependent on the Eigenparameter

Non-Self-Adjoint Singular Sturm-Liouville Problems with Boundary Conditions Dependent on the Eigenparameter

Let 𝐴 denote the operator generated in 𝐿2(ℛ+) by the Sturm-Liouville problem: −𝑦+𝑞(𝑥)𝑦=𝜆2𝑦, 𝑥∈ℛ+=[0,∞), (𝑦/𝑦)(0)=(𝛽1𝜆+𝛽0)/(𝛼1𝜆+𝛼0), where 𝑞 is a complex valued function and 𝛼0,𝛼1,𝛽0,𝛽1∈𝒞, with 𝛼0𝛽1−𝛼1𝛽0≠0. In this paper, using the uniqueness theorems of analytic functions, we investigate the eige...

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Main Authors: Elgiz Bairamov, M. Seyyit Seyyidoglu
Format: Article
Language:English
Published: Hindawi Limited 2010-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2010/982749
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spelling doaj-9d164ac142424477a2d4375c39c5a5d72020-11-24T23:17:01ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092010-01-01201010.1155/2010/982749982749Non-Self-Adjoint Singular Sturm-Liouville Problems with Boundary Conditions Dependent on the EigenparameterElgiz Bairamov0M. Seyyit Seyyidoglu1Department of Mathematics, Science Faculty, Ankara University, 06100 Ankara, TurkeyDepartment of Mathematics, Science and Art Faculty, Usak University, 64200 Campus-Uşak, TurkeyLet 𝐴 denote the operator generated in 𝐿2(ℛ+) by the Sturm-Liouville problem: −𝑦+𝑞(𝑥)𝑦=𝜆2𝑦, 𝑥∈ℛ+=[0,∞), (𝑦/𝑦)(0)=(𝛽1𝜆+𝛽0)/(𝛼1𝜆+𝛼0), where 𝑞 is a complex valued function and 𝛼0,𝛼1,𝛽0,𝛽1∈𝒞, with 𝛼0𝛽1−𝛼1𝛽0≠0. In this paper, using the uniqueness theorems of analytic functions, we investigate the eigenvalues and the spectral singularities of 𝐴. In particular, we obtain the conditions on 𝑞 under which the operator 𝐴 has a finite number of the eigenvalues and the spectral singularities.http://dx.doi.org/10.1155/2010/982749
collection DOAJ
language English
format Article
sources DOAJ
author Elgiz Bairamov
M. Seyyit Seyyidoglu
spellingShingle Elgiz Bairamov
M. Seyyit Seyyidoglu
Non-Self-Adjoint Singular Sturm-Liouville Problems with Boundary Conditions Dependent on the Eigenparameter
Abstract and Applied Analysis
author_facet Elgiz Bairamov
M. Seyyit Seyyidoglu
author_sort Elgiz Bairamov
title Non-Self-Adjoint Singular Sturm-Liouville Problems with Boundary Conditions Dependent on the Eigenparameter
title_short Non-Self-Adjoint Singular Sturm-Liouville Problems with Boundary Conditions Dependent on the Eigenparameter
title_full Non-Self-Adjoint Singular Sturm-Liouville Problems with Boundary Conditions Dependent on the Eigenparameter
title_fullStr Non-Self-Adjoint Singular Sturm-Liouville Problems with Boundary Conditions Dependent on the Eigenparameter
title_full_unstemmed Non-Self-Adjoint Singular Sturm-Liouville Problems with Boundary Conditions Dependent on the Eigenparameter
title_sort non-self-adjoint singular sturm-liouville problems with boundary conditions dependent on the eigenparameter
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2010-01-01
description Let 𝐴 denote the operator generated in 𝐿2(ℛ+) by the Sturm-Liouville problem: −𝑦+𝑞(𝑥)𝑦=𝜆2𝑦, 𝑥∈ℛ+=[0,∞), (𝑦/𝑦)(0)=(𝛽1𝜆+𝛽0)/(𝛼1𝜆+𝛼0), where 𝑞 is a complex valued function and 𝛼0,𝛼1,𝛽0,𝛽1∈𝒞, with 𝛼0𝛽1−𝛼1𝛽0≠0. In this paper, using the uniqueness theorems of analytic functions, we investigate the eigenvalues and the spectral singularities of 𝐴. In particular, we obtain the conditions on 𝑞 under which the operator 𝐴 has a finite number of the eigenvalues and the spectral singularities.
url http://dx.doi.org/10.1155/2010/982749
work_keys_str_mv AT elgizbairamov nonselfadjointsingularsturmliouvilleproblemswithboundaryconditionsdependentontheeigenparameter
AT mseyyitseyyidoglu nonselfadjointsingularsturmliouvilleproblemswithboundaryconditionsdependentontheeigenparameter
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