Advanced search
Publication Cover
Inverse Problems in Science and Engineering Volume 18, 2010 - Issue 1: Proceedings of the 4th International Conference on Inverse Problems: Modelling and Simulation, May 26th–30th, 2008, held in Fethiye, Turkey
Submit an article Journal homepage
313
Views
11
CrossRef citations to date
0
Altmetric
Original Articles

Reconstruction formula for the potential function of Sturm–Liouville problem with eigenparameter boundary condition

Etibar S. PanakhovDepartment of Mathematics, Firat University, 23119 Elazιg, Turkey
,
Hikmet KoyunbakanDepartment of Mathematics, Firat University, 23119 Elazιg, Turkey
&
Unal IcDepartment of Mathematics, Firat University, 23119 Elazιg, Turkey
Pages 173-180 | Received 15 Oct 2008, Accepted 28 Mar 2009, Published online: 19 Oct 2009

References

  • Borg, G, 1945. Eine umkehrung der Sturm-Liouvillesehen eigenwertaufgabe, Acta Math. 78 (1945), pp. 1–96.
  • Hochstadt, H, 1973. The inverse Sturm–Liouville problem, Commun. Pure Appl. Math. 26 (1973), pp. 715–729.
  • Gelfand, IM, and Levitan, BM, 1951. On the determination of a differential equation from its spectral function, Amer. Math Soc. Trans. 1 (1951), pp. 253–304.
  • Gesztesy, F, and Simon, B, 2000. Inverse spectral analysis with partial information on the potential. II: The case of discrete spectrum, Trans. Am. Math. Soc. 352 (2000), pp. 2765–2787.
  • Gesztesy, F, and Simon, B, 2000. On local Borg–Marchenko uniqueness results, Commun. Math. Phys. 211 (2) (2000), pp. 273–287.
  • Malamud, MM, 1999. Uniqueness questions in inverse problems for systems of differential equations on a finite interval, Trans. Moscow Math Soc. 60 (1999), pp. 204–262.
  • McLaughlin, JR, 1988. Inverse spectral theory using nodal points as data–a uniqueness result, J. Diff. Eq. 73 (1988), pp. 354–362.
  • Hald, O, and McLaughlin, JR, 1989. Solutions of inverse nodal problems, Inv. Prob. 5 (1989), pp. 307–347.
  • Browne, PJ, and Sleeman, BD, 1996. Inverse nodal problem for Sturm–Liouville equation with eigenparameter depend boundary conditions, Inverse Problems 12 (1996), pp. 377–381.
  • Yang, X-F, 1997. A solution of the inverse nodal problem, Inv. Probl. 13 (1997), pp. 203–213.
  • Cheng, YH, Law, C-K, and Tsay, J, 2000. Remarks on a new inverse nodal problem, J. Math. Anal. Appl. 248 (2000), pp. 145–155.
  • Koyunbakan, H, 2005. Inverse nodal problem for singular differential operator, J. Inverse Ill-posed Probl. 13 (5) (2005), pp. 435–440.
  • Hochstadt, H, 1967. On inverse problems associated with second-order differential operators, Acta Math. 119 (1967), pp. 173–192.
  • Shen, CL, and Tsai, TM, 1995. On a uniform approximation of the density function of a string equation using eigenvalues and nodal points and some related inverse nodal problems, Inv. Prob. 11 (1995), pp. 1113–1123.
  • Chen, Y-T, Cheng, YH, Law, CK, and Tsa, J, 2002. Convergence of the reconstruction formula for the potential function, Proc. Amer. Math. Soc. 130 (2002), pp. 2319–2324.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.