Spectral Properties of the Anti-Periodic Boundary-Value-Transition Problems
This work is concerned with the boundary-value-transition problem consisting of atwo-interval Sturm-Liouville equationLu ≔ −u′′(x) + q(x)u(x) = λu(x) , x ∈ [−1,0) ∪ (0,1]together with anti-periodic boundary conditions, given byu(−1) = −u(1)u′(−1) = −u′(1)and transition conditions at the interior poi...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Naim Çağman
2020-12-01
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| Series: | Journal of New Theory |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/en/download/article-file/1371909 |
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| Summary: | This work is concerned with the boundary-value-transition problem consisting of atwo-interval Sturm-Liouville equationLu ≔ −u′′(x) + q(x)u(x) = λu(x) , x ∈ [−1,0) ∪ (0,1]together with anti-periodic boundary conditions, given byu(−1) = −u(1)u′(−1) = −u′(1)and transition conditions at the interior point x = 0, given byu(+0) = Ku(−0)u′(+0) =1/Ku′(−0)where q(x) is a continuous function in the intervals [−1,0) and (0,1] with finite limit values q(±0) ,K ≠ 0 is the real number and λ is the complex eigenvalue parameter. In this study we shall investigatesome properties of the eigenvalues and eigenfunctions of the considered problem. |
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| ISSN: | 2149-1402 |