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 |
| Summary: | 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. |
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| ISSN: | 2322-5807 2423-3900 |