Higher-order Sturm–Liouville problems with the same eigenvalues

Abstract

In this paper, we consider self-adjoint Sturm–Liouville problem (SLP) of higher-order. We define anequivalence relation between second- and higher-order SLP. Using the Darboux lemma and equivalence relation weobtain the closed form of a family of SLP which have the same eigenvalues. Also, some spectral properties of this familyof Sturm–Liouville problems are investigated.