Ambarzumyan Type Theorems for a Class of Sturm-Liouville Problem

Yıl 2017, Cilt: 38 Sayı: 3, 396 - 399, 30.09.2017

A. Sinan Özkan Yaşar Çakmak

https://doi.org/10.17776/csj.340393

Öz

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

Anahtar Kelimeler

Ambarzumyan theorem, Sturm-Liouville equation, Inverse problem

Bir Sınıf Sturm-Liouville Problemi için Ambarzumyan Tipi Teoremler

Öz

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

Anahtar Kelimeler

Ambarzumyan teoremi, Sturm-Liouville denklemi, Ters problem

Kaynakça

• [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