Uniqueness of Inverse Sturm-Liouville Problems with Two Delta Interaction Points

Year 2021, Volume: 2 Issue: 1, 42 - 51, 29.01.2021

Manaf Manaflı , Ahmet Zincir

Abstract

We establish various uniqueness results for inverse spectral problems of Sturm-Liouville equations with two delta-interaction points.

Keywords

Uniqueness resuls;, Strum-Liouville problems;, Point delta interactions.

References

• [1] Albeverio S., Gesztesy F., Hoegh-Krohn R., Holden H., (with an appendix by Exner P.), Solvable Models in Quantum Mechanics (2nd Edition), AMS Chelsea Publishing, 2005.
• [2] Amirov R. Kh., On Sturm-Liouville operators with discontinuity conditions inside an interval, Journal of Mathematical Analysis and Applications, 317, 163-176, 2006.
• [3] Bellman R., Cooke K., Differantial-Difference Equations, Academic Press, 1963.
• [4] Coddington E.A., Levinson N., Theory of Ordinary Differantial Equations, McGraw-Hill, 1955.
• [5] Conway J.B., Functions of One Complex Variable (2nd Edition), Springer, 1995.
• [6] Freiling G., Yurko V.A., Inverse Sturm-Liouville Problems and Their Applications, Nova Science Publishers, Inc., 2001.
• [7] Guo Y., Wei G., On the reconstruction of the Sturm-Liouville problems with spectral parameter in the discontinuity conditions, Results in Mathematics, 65, 385-398, 2014.
• [8] Hald O.H., Discontinuous inverse eigenvalue problems, Communications on Pure and Applied Mathematics, 37(5), 53-72, 1986.
• [9] Levitan B.M., Inverse Sturm-Liouville Problems. VSP: Zeist, 1987.
• [10] Liu Y., Shi G., Yan J., An inverse problem for non-selfadjoint Sturm-Liouville operator with discontinuity conditions inside a nite interval, Inverse Problems in Science and Engineering, 27(3), 407-421, 2019.
• [11] Manafov M. Dzh., Inverse spectral problems for energy-dependent Sturm-Liouville equations with nitely many point  -interactions, Electronic Journal of Dierential Equations, 11, 1-12, 2016.
• [12] Manafov M. Dzh., Inverse spectral problems for energy-dependent Sturm-Liouville equations with delta - interaction, Filomat, 30(11), 2935-2946, 2016.
• [13] Manafov M. Dzh., Inverse spectral and inverse nodal problems for Sturm-Liouville equations with point delta and delta ′-interactions, Proceedings of the Institute of Mathematics and Mechanics, 45(2), 286-294, 2019.
• [14] Marchenko V.A., Sturm-Liouville Operators and Their Applications, Operator Theory: Advanced and Application, Birkhauser, 1986.
• [15] Xu X-Ch., Yang Ch-F., Inverse spectral problems for the Sturm-Liouville operator with discontinuity, Journal of Dierential Equations, 262, 3093-3106, 2017.
• [16] Yurko V.A., Boundary value problems with discontinuity conditions in an interior point of the interval, Dierential Equations, 36(8), 1139-1140, 2000.