Eigenfunction Expansions for Second-Order Boundary Value Problems with Separated Boundary Conditions
In this paper, we investigate some properties of eigenvalues and eigenfunctions of boundary value problems with separated boundary conditions. Also, we obtain formal series solutions for some partial differential equations associated with the second order differential equation, and study necessary a...
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| Format: | Article |
| Language: | English |
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University of Kashan
2016-07-01
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| Series: | Mathematics Interdisciplinary Research |
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| Online Access: | https://mir.kashanu.ac.ir/article_33850_0af3a4d1236273501fd68bad66d189f3.pdf |
| _version_ | 1797630989738967040 |
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| author | Seyfollah Mosazadeh |
| author_facet | Seyfollah Mosazadeh |
| author_sort | Seyfollah Mosazadeh |
| collection | DOAJ |
| description | In this paper, we investigate some properties of eigenvalues and eigenfunctions of boundary value problems with separated boundary conditions. Also, we obtain formal series solutions for some partial differential equations associated with the second order differential equation, and study necessary and sufficient conditions for the negative and positive eigenvalues of the boundary value problem. Finally, by the sequence of orthogonal eigenfunctions, we provide the eigenfunction expansions for twice continuously differentiable functions. |
| first_indexed | 2024-03-11T11:15:43Z |
| format | Article |
| id | doaj.art-a991a0c8f72841108270ce34e154b0df |
| institution | Directory Open Access Journal |
| issn | 2476-4965 |
| language | English |
| last_indexed | 2024-03-11T11:15:43Z |
| publishDate | 2016-07-01 |
| publisher | University of Kashan |
| record_format | Article |
| series | Mathematics Interdisciplinary Research |
| spelling | doaj.art-a991a0c8f72841108270ce34e154b0df2023-11-11T06:27:33ZengUniversity of KashanMathematics Interdisciplinary Research2476-49652016-07-011232533410.22052/mir.2016.3385033850Eigenfunction Expansions for Second-Order Boundary Value Problems with Separated Boundary ConditionsSeyfollah Mosazadeh0Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, I. R. IranIn this paper, we investigate some properties of eigenvalues and eigenfunctions of boundary value problems with separated boundary conditions. Also, we obtain formal series solutions for some partial differential equations associated with the second order differential equation, and study necessary and sufficient conditions for the negative and positive eigenvalues of the boundary value problem. Finally, by the sequence of orthogonal eigenfunctions, we provide the eigenfunction expansions for twice continuously differentiable functions.https://mir.kashanu.ac.ir/article_33850_0af3a4d1236273501fd68bad66d189f3.pdfboundary value problemeigenvalueeigenfunctioncompletenesseigenfunction expansion |
| spellingShingle | Seyfollah Mosazadeh Eigenfunction Expansions for Second-Order Boundary Value Problems with Separated Boundary Conditions Mathematics Interdisciplinary Research boundary value problem eigenvalue eigenfunction completeness eigenfunction expansion |
| title | Eigenfunction Expansions for Second-Order Boundary Value Problems with Separated Boundary Conditions |
| title_full | Eigenfunction Expansions for Second-Order Boundary Value Problems with Separated Boundary Conditions |
| title_fullStr | Eigenfunction Expansions for Second-Order Boundary Value Problems with Separated Boundary Conditions |
| title_full_unstemmed | Eigenfunction Expansions for Second-Order Boundary Value Problems with Separated Boundary Conditions |
| title_short | Eigenfunction Expansions for Second-Order Boundary Value Problems with Separated Boundary Conditions |
| title_sort | eigenfunction expansions for second order boundary value problems with separated boundary conditions |
| topic | boundary value problem eigenvalue eigenfunction completeness eigenfunction expansion |
| url | https://mir.kashanu.ac.ir/article_33850_0af3a4d1236273501fd68bad66d189f3.pdf |
| work_keys_str_mv | AT seyfollahmosazadeh eigenfunctionexpansionsforsecondorderboundaryvalueproblemswithseparatedboundaryconditions |