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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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2010/982749 |
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| author | Elgiz Bairamov M. Seyyit Seyyidoglu |
| author_facet | Elgiz Bairamov M. Seyyit Seyyidoglu |
| author_sort | Elgiz Bairamov |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-9d164ac142424477a2d4375c39c5a5d7 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-9d164ac142424477a2d4375c39c5a5d72025-02-03T01:00:21ZengWileyAbstract 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 |
| spellingShingle | Elgiz Bairamov M. Seyyit Seyyidoglu Non-Self-Adjoint Singular Sturm-Liouville Problems with Boundary Conditions Dependent on the Eigenparameter Abstract and Applied Analysis |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/2010/982749 |
| work_keys_str_mv | AT elgizbairamov nonselfadjointsingularsturmliouvilleproblemswithboundaryconditionsdependentontheeigenparameter AT mseyyitseyyidoglu nonselfadjointsingularsturmliouvilleproblemswithboundaryconditionsdependentontheeigenparameter |