Reconstruction of Potential in Discrete Sturm–Liouville Problem

• Koyunbakan, Hikmet ^[1]
  1. [1] Fırat University

     Fırat University

     Turquía

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 1, 2022
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • In this paper, we consider the Sturm–Liouville problem with Dirichlet conditions in the case of time scales consists isolated points. Then, we obtain discrete Sturm–Liouville problem on a finite interval. We solve the inverse nodal problem, especially give a reconstruction formula for the potential function q.

• Referencias bibliográficas
  • 1. Bohner, M., Peterson, A.: Dynamic Equations on Time Scales: An Introduction with Applications. Birkhauser, Boston (2001)
  • 2. Hilger, S.: Ein Masskettenkalkul mit Anwendung auf Zentrumsmannigfaltigkeiten. PhD, Universitat Wurzburg, Wurzburg, Germany (1988) (in...
  • 3. Kelley, W.G., Peterson, A.C.: Difference Equations: An Introduction with Applications, 2nd edn. Academic Press, San Diego (2001)
  • 4. Agarwal, R.P., Bohner, M., Wong, P.J.Y.: Eigenvalues and eigenfunctions of discrete conjugate boundary value problems. Comput. Math. Appl....
  • 5. Allahverdiev, B., Eryilmaz, A., Tuna, H.: Dissipative Sturm-Liouville operators with a spectral parameter in the boundary condition on...
  • 6. Bala, B., Kablan, A., Manafov, M.: Direct and inverse spectral problems for discrete Sturm-Liouville problem with generalized function...
  • 7. Bohner, M.: On disconjugacy for Sturm-Liouville difference equations. J. Differ. Equ. Appl. 2(2), 227–237 (1996)
  • 8. Bohner, M.: Asymptotic behavior of discretized Sturm-Liouville eigenvalue problems. J. Differ. Equ. Appl. 3, 289–295 (1998)
  • 9. Bohner, M.: Discrete Sturmian theory. Math. Inequ. Appl. 1(3), 375–383 (1998)
  • 10. Bohner, M., Koyunbakan, H.: Inverse problems for Sturm-Liouville difference equations. Filomat 30(5), 1297–1304 (2016)
  • 11. Ahlbrandt, C., Bohner, M., Voepel, T.: Variable change for Sturm-Liouville differential expressions on time scales. J. Differ. Equ. Appl....
  • 12. Currie, S., Love, A.: Inverse problems for difference equations with quadratic eigenparameter dependent boundary conditions II. Adv. Pure...
  • 13. Gao, C., Ma, R.: Eigenvalues of discrete Sturm-Liouville problems with eigenparameter dependent boundary conditions. Linear Algebra Appl....
  • 14. Yilmaz, E., Gulsen, T., Koyunbakan, H.: Conformable fractional Sturm-Liouville equation and some existence results on time scales. Turkish...
  • 15. Ambartsumyan, V.A.: Über eine Frage der Eigenwerttheorie. Zeitschrift für Physik 53, 690–695 (1929)
  • 16. Buterin, S.A., Shieh, C.T.: Incomplete inverse spectral and nodal problems for differential pencils. Results Math. 62(1–2), 167–179 (2012)
  • 17. Hald, O., McLaughlin, J.R.: Solution of the inverse nodal problems. Inverse Probl. 5, 307–347 (1989)
  • 18. Hu, Y.T., Bondarenko, N.P., Shieh, C.T., Yang, C.F.: Traces and inverse nodal problems for Dirac-type integro-differential operators on...
  • 19. Zhang, R., Sat, M., Yang, C.F.: Inverse nodal problem for the Sturm-Liouville operator with a weightAppl. Math. J. Chinese Univ. 35(2),...
  • 20. Hu, Y.T., Bondarenko, N.P., Yang, C.F.: Traces and inverse nodal problem for Sturm-Liouville operators with frozen argument. Appl. Math....
  • 21. Yang, C.F., Xu, X.C., Buterin, S.A.: Solution to the interior transmission problem using nodes on a subinterval as input data. Nonlinear...
  • 22. Law, C.K., Yang, C.F.: Reconstruction of the potential function and its derivatives using nodal data. Inverse Probl. 14, 299–312 (1998)
  • 23. McLaughlin, J.R.: Inverse spectral theory using nodal points as data-a uniqueness result. J. Differ. Equ. 73, 354–362 (1988)
  • 24. Sadovnichii, V.A., Sultanaev, Y.T., Akhtyamov, A.M.: Solvability theorems for an inverse nonselfadjoint Sturm-Liouville problem with nonseparated...
  • 25. Shen, C.L.: On the nodal sets of the eigenfunctions of the string equations. SIAM J. Math. Anal. 19(89), 1419–1424 (1988)
  • 26. Kratz,W.: Quadratic Functionals in Variational Analysis and Control Theory, volume 6 ofMathematical Topics. Akademie Verlag (1995)
  • 27. Paine, J.W., Anderssen, R.S., De Hoog, F.R.: On the correction of finite difference eigenvalue approximations for Sturm-Liouville problems....
  • 28. Anderssen, R.S., De Hoog, F.R.: On the correction of finite difference eigenvalue approximation for Sturm-Liouville problems with general...
  • 29. Anderssen, R.S., De Hoog, F.R.: Asymtotic formulas for discrete eigenvalue problems in Liouville normal form. Math. Models Methods Appl....
  • 30. Elaydi, S.: An Introduction to Difference Equations. Third Edition Springer (1996)