Uniqueness of Inverse Sturm-Liouville Problems with Two Delta Interaction Points
Uniqueness of Inverse Sturm-Liouville Problems with Two Delta Interaction Points
We establish various uniqueness results for inverse spectral problems of Sturm-Liouville equations with two delta-interaction points.
___
- [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.