Open Access

ARTICLE

Ambarzumyan Type Theorem For a Matrix Valued Quadratic Sturm-Liouville Problem

Emrah Yilmaz¹, Hikmet Koyunbakan²
1 Firat University, Department of Mathematics, Elazıg, TURKEY, emrah231983@gmail.com
2 Firat University, Department of Mathematics, Elazıg, TURKEY, hkoyunbakan@gmail.com

Computer Modeling in Engineering & Sciences 2014, 99(6), 463-471. https://doi.org/10.3970/cmes.2014.099.463

Abstract

In this study, Ambarzumyan’s theorem for quadratic Sturm-Liouville problem is extended to second order differential systems of dimension d ≥ 2. It is shown that if the spectrum is the same as the spectrum belonging to the zero potential, then the matrix valued functions both P(x) and Q(x) are zero by imposing a condition on P(x). In scaler case, this problem was solved in [Koyunbakan, Lesnic and Panakhov (2013)].

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Keywords

Matrix quadratic Sturm-Liouville equation, spectrum, Ambarzumyan’s theorem.

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