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 an equivalence relation between second- and higher-order SLP. Using the Darboux lemma and equivalence relation we obtain the closed form of a family of SLP which have the same eigenvalues. Also, some spectral properties of this family of Sturm–Liouville problems are investigated.