Inverse Sturm-Liouville problem with discontinuity conditions
This paper deals with the boundary value problem involving the dierential equation ly := -y''+qy = λy, subject to the standard boundary conditions along with the following discontinuity conditions at a point a ε(0,π) y(a + 0) = a1y(a - 0), y'(a + 0) = a1-1y'(a - 0) +...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Maragheh
2014-02-01
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| Series: | Sahand Communications in Mathematical Analysis |
| Subjects: | |
| Online Access: | http://scma.maragheh.ac.ir/article_11264_1863.html |
| _version_ | 1818682614590996480 |
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| author | Mohammad Shahriari Aliasghar Jodayree Akbarfam |
| author_facet | Mohammad Shahriari Aliasghar Jodayree Akbarfam |
| author_sort | Mohammad Shahriari |
| collection | DOAJ |
| description | This paper deals with the boundary value problem involving the dierential equation
ly := -y''+qy = λy,
subject to the standard boundary conditions along with the following
discontinuity conditions at a point a ε(0,π)
y(a + 0) = a1y(a - 0), y'(a + 0) = a1-1y'(a - 0) + a2y(a - 0),
where q(x), a1,a2 are real, q ε L2(0,π ) and λ is a parameter independent of x. We develop the Hochestadt's result based on the transformation operator for inverse Sturm-Liouville problem when there are discontinuous conditions. Furthermore, we establish a formula for q(x) - q~(x) in the nite interval where q(x) and q~(x) are analogous functions. |
| first_indexed | 2024-12-17T10:21:39Z |
| format | Article |
| id | doaj.art-6d1924113d904807aa5da43b3ed67727 |
| institution | Directory Open Access Journal |
| issn | 2322-5807 2423-3900 |
| language | English |
| last_indexed | 2024-12-17T10:21:39Z |
| publishDate | 2014-02-01 |
| publisher | University of Maragheh |
| record_format | Article |
| series | Sahand Communications in Mathematical Analysis |
| spelling | doaj.art-6d1924113d904807aa5da43b3ed677272022-12-21T21:52:46ZengUniversity of MaraghehSahand Communications in Mathematical Analysis2322-58072423-39002014-02-01112940Inverse Sturm-Liouville problem with discontinuity conditionsMohammad Shahriari 0Aliasghar Jodayree Akbarfam1Department of Mathematics, Faculty of Science, University of Maragheh, P.O. Box 55181-83111, Maragheh, Iran.Faculty of Mathematical Sciences, University of Tabriz, Tabriz 51664, Iran.This paper deals with the boundary value problem involving the dierential equation ly := -y''+qy = λy, subject to the standard boundary conditions along with the following discontinuity conditions at a point a ε(0,π) y(a + 0) = a1y(a - 0), y'(a + 0) = a1-1y'(a - 0) + a2y(a - 0), where q(x), a1,a2 are real, q ε L2(0,π ) and λ is a parameter independent of x. We develop the Hochestadt's result based on the transformation operator for inverse Sturm-Liouville problem when there are discontinuous conditions. Furthermore, we establish a formula for q(x) - q~(x) in the nite interval where q(x) and q~(x) are analogous functions.http://scma.maragheh.ac.ir/article_11264_1863.htmlInverse problemSturm-Liouville problemsDiscontinuous conditionsGreen's function |
| spellingShingle | Mohammad Shahriari Aliasghar Jodayree Akbarfam Inverse Sturm-Liouville problem with discontinuity conditions Sahand Communications in Mathematical Analysis Inverse problem Sturm-Liouville problems Discontinuous conditions Green's function |
| title | Inverse Sturm-Liouville problem with discontinuity conditions |
| title_full | Inverse Sturm-Liouville problem with discontinuity conditions |
| title_fullStr | Inverse Sturm-Liouville problem with discontinuity conditions |
| title_full_unstemmed | Inverse Sturm-Liouville problem with discontinuity conditions |
| title_short | Inverse Sturm-Liouville problem with discontinuity conditions |
| title_sort | inverse sturm liouville problem with discontinuity conditions |
| topic | Inverse problem Sturm-Liouville problems Discontinuous conditions Green's function |
| url | http://scma.maragheh.ac.ir/article_11264_1863.html |
| work_keys_str_mv | AT mohammadshahriari inversesturmliouvilleproblemwithdiscontinuityconditions AT aliasgharjodayreeakbarfam inversesturmliouvilleproblemwithdiscontinuityconditions |