Research Article

An inverse nodal problem for differential pencils with complex spectral parameter dependent boundary conditions

Volume: 5 Number: 1 January 1, 2017
EN

An inverse nodal problem for differential pencils with complex spectral parameter dependent boundary conditions

Abstract

In this study, we are concerned with an inverse nodal problem for second order differential pencil on a finite interval with complex spectral parameter dependent boundary conditions by using nodal points. We give some reconstruction formulas for potential functions  and  as a limit.

Keywords

References

  1. V. A. Ambartsumyan, Über eine Frage der Eigenwerttheorie, Zeitschrift für Physik, (1929) 53, 690-695.
  2. B. M. Levitan and I. S. Sargsjan, Introduction to Spectral Theory: Self Adjoint Ordinary Differential Operators, American Mathematical Society, Providence, Rhode Island, (1975).
  3. V. Pivovarchik, Direct and inverse three-point Sturm-Liouville problems with parameter dependent boundary conditions, Asymptotic Analysis, (2001) 26(3-4), 219–238.
  4. C. T. Shieh, S. A. Buterin and M. Ignatiev, On Hochstadt-Lieberman theorem for Sturm-Liouville operators, Far East Journal of Applied Mathematics, (2011) 52(2), 131-146.
  5. R. Hryniv and N. Pronska, Inverse spectral problems for energy-dependent Sturm-Liouville equations, Inverse Problems, (2012) 28(8), 085008.
  6. G. Freiling and V. A. Yurko, Inverse Sturm-Liouville problems and their applications, NOVA Science Publishers, New York, (2001).
  7. J. Pöschel and E. Trubowitz, Inverse spectral theory, volume 130 of Pure and Applied Mathematics, Academic Press, Inc, Boston, MA, (1987).
  8. J. R. McLaughlin, Inverse spectral theory using nodal points as data-a uniqueness result, Journal of Differential Equations, (1988) 73(2), 354-362.

Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

Tuba Gulsen * This is me
Türkiye

Hikmet Koyunbakan This is me
Türkiye

Publication Date

January 1, 2017

Submission Date

October 24, 2016

Acceptance Date

December 19, 2016

Published in Issue

Year 1970 Volume: 5 Number: 1

APA
Gulsen, T., Yilmaz, E., & Koyunbakan, H. (2017). An inverse nodal problem for differential pencils with complex spectral parameter dependent boundary conditions. New Trends in Mathematical Sciences, 5(1), 137-144. https://izlik.org/JA77ML27MJ
AMA
1.Gulsen T, Yilmaz E, Koyunbakan H. An inverse nodal problem for differential pencils with complex spectral parameter dependent boundary conditions. New Trends in Mathematical Sciences. 2017;5(1):137-144. https://izlik.org/JA77ML27MJ
Chicago
Gulsen, Tuba, Emrah Yilmaz, and Hikmet Koyunbakan. 2017. “An Inverse Nodal Problem for Differential Pencils With Complex Spectral Parameter Dependent Boundary Conditions”. New Trends in Mathematical Sciences 5 (1): 137-44. https://izlik.org/JA77ML27MJ.
EndNote
Gulsen T, Yilmaz E, Koyunbakan H (January 1, 2017) An inverse nodal problem for differential pencils with complex spectral parameter dependent boundary conditions. New Trends in Mathematical Sciences 5 1 137–144.
IEEE
[1]T. Gulsen, E. Yilmaz, and H. Koyunbakan, “An inverse nodal problem for differential pencils with complex spectral parameter dependent boundary conditions”, New Trends in Mathematical Sciences, vol. 5, no. 1, pp. 137–144, Jan. 2017, [Online]. Available: https://izlik.org/JA77ML27MJ
ISNAD
Gulsen, Tuba - Yilmaz, Emrah - Koyunbakan, Hikmet. “An Inverse Nodal Problem for Differential Pencils With Complex Spectral Parameter Dependent Boundary Conditions”. New Trends in Mathematical Sciences 5/1 (January 1, 2017): 137-144. https://izlik.org/JA77ML27MJ.
JAMA
1.Gulsen T, Yilmaz E, Koyunbakan H. An inverse nodal problem for differential pencils with complex spectral parameter dependent boundary conditions. New Trends in Mathematical Sciences. 2017;5:137–144.
MLA
Gulsen, Tuba, et al. “An Inverse Nodal Problem for Differential Pencils With Complex Spectral Parameter Dependent Boundary Conditions”. New Trends in Mathematical Sciences, vol. 5, no. 1, Jan. 2017, pp. 137-44, https://izlik.org/JA77ML27MJ.
Vancouver
1.Tuba Gulsen, Emrah Yilmaz, Hikmet Koyunbakan. An inverse nodal problem for differential pencils with complex spectral parameter dependent boundary conditions. New Trends in Mathematical Sciences [Internet]. 2017 Jan. 1;5(1):137-44. Available from: https://izlik.org/JA77ML27MJ