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

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)].