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Ambarzumyan Type Theorems for a Class of Sturm-Liouville Problem

Year 2017, , 396 - 399, 30.09.2017
https://doi.org/10.17776/csj.340393

Abstract

In this paper, we prove Ambarzumyan type theorems for
an impulsive Sturm–Liouville problem with eigenparameter in the boundary
conditions.

References

  • [1]. Ambartsumyan, V. A., Uber eine frage der eigenwerttheorie, Zeitschrift für Physik, 1929, 53, 690-695.
  • [2]. Chern, H. H., Law, C. K., Wang, H.J., Corrigendum to extension of Ambarzumyan’s theorem to general boundary conditions, J. Math. Anal. Appl., 2005, 309, 764-768.
  • [3]. Yang, C. F. and Yang, X. P., Ambarzumyan’s theorem with eigenparameter in the boundary conditions, Acta Math. Sci., 2011, 31B(4), 1561-1568.
  • [4]. Yurko, V. A., On Ambarzumyan-type theorems, Applied Math. Letters, 2013, 26, 506-509.
  • [5]. Yang, C. F. and Yang, X. P., Ambarzumyan’s theorems for Sturm-Liouville operators with general boundary conditions, Acta Math. Sci., 2010, 30A(2), 449-455.
  • [6]. Horváth, M., On a theorem of Ambarzumyan, Proc. Roy. Soc.Edinburgh Sect. A, 2001, 131(4), 899-907.
  • [7]. Yang, C. F. and Yang, X. P., Some Ambarzumyan-type theorems for Dirac operators, Inverse Problems, 2009, 25(9), 095012pp.13.
  • [8]. Chern, H. H. and Shen, C. L., On the n-dimensional Ambarzumyan’s theorem, Inverse Problems, 1997, 13, 15-18.
  • [9]. Márton, K., An n-dimensional Ambarzumyan type theorem for Dirac operators, Inverse Problems, 2004, 20, 1593-1597.
  • [10]. Yang, C. F., Huang, Z. Y. and Yang, X. P., Ambarzumyan’s theorems for vectorial Sturm-Liouville systems with coupled boundary conditions, Taiwanese J. Math., 2010, 14(4), 1429-1437.
  • [11]. Kırac, A. A., On the Ambarzumyan’s theorem for the quasi-periodic problem, Analysis and Math. Physics, 2015, 13, 15-18.
  • [12]. Freiling, G. and Yurko, V. A., Inverse Sturm–Liouville problems and their applications, Nova Science, Huntington, NY, 2001

Bir Sınıf Sturm-Liouville Problemi için Ambarzumyan Tipi Teoremler

Year 2017, , 396 - 399, 30.09.2017
https://doi.org/10.17776/csj.340393

Abstract

Bu makalede, sınır koşulları parametreye bağlı, bir
geçiş koşullu Sturm–Liouville problemi için Ambarzumyan tipi teoremler
ispatlanmaktadır. 

References

  • [1]. Ambartsumyan, V. A., Uber eine frage der eigenwerttheorie, Zeitschrift für Physik, 1929, 53, 690-695.
  • [2]. Chern, H. H., Law, C. K., Wang, H.J., Corrigendum to extension of Ambarzumyan’s theorem to general boundary conditions, J. Math. Anal. Appl., 2005, 309, 764-768.
  • [3]. Yang, C. F. and Yang, X. P., Ambarzumyan’s theorem with eigenparameter in the boundary conditions, Acta Math. Sci., 2011, 31B(4), 1561-1568.
  • [4]. Yurko, V. A., On Ambarzumyan-type theorems, Applied Math. Letters, 2013, 26, 506-509.
  • [5]. Yang, C. F. and Yang, X. P., Ambarzumyan’s theorems for Sturm-Liouville operators with general boundary conditions, Acta Math. Sci., 2010, 30A(2), 449-455.
  • [6]. Horváth, M., On a theorem of Ambarzumyan, Proc. Roy. Soc.Edinburgh Sect. A, 2001, 131(4), 899-907.
  • [7]. Yang, C. F. and Yang, X. P., Some Ambarzumyan-type theorems for Dirac operators, Inverse Problems, 2009, 25(9), 095012pp.13.
  • [8]. Chern, H. H. and Shen, C. L., On the n-dimensional Ambarzumyan’s theorem, Inverse Problems, 1997, 13, 15-18.
  • [9]. Márton, K., An n-dimensional Ambarzumyan type theorem for Dirac operators, Inverse Problems, 2004, 20, 1593-1597.
  • [10]. Yang, C. F., Huang, Z. Y. and Yang, X. P., Ambarzumyan’s theorems for vectorial Sturm-Liouville systems with coupled boundary conditions, Taiwanese J. Math., 2010, 14(4), 1429-1437.
  • [11]. Kırac, A. A., On the Ambarzumyan’s theorem for the quasi-periodic problem, Analysis and Math. Physics, 2015, 13, 15-18.
  • [12]. Freiling, G. and Yurko, V. A., Inverse Sturm–Liouville problems and their applications, Nova Science, Huntington, NY, 2001
There are 12 citations in total.

Details

Journal Section Articles
Authors

A. Sinan Özkan

Yaşar Çakmak

Publication Date September 30, 2017
Submission Date August 3, 2017
Acceptance Date September 14, 2017
Published in Issue Year 2017

Cite

APA Özkan, A. S., & Çakmak, Y. (2017). Ambarzumyan Type Theorems for a Class of Sturm-Liouville Problem. Cumhuriyet Science Journal, 38(3), 396-399. https://doi.org/10.17776/csj.340393