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.
"Higher-order Sturm-Liouville problems with the same eigenvalues,"
Turkish Journal of Mathematics: Vol. 44:
2, Article 6.
Available at: https://journals.tubitak.gov.tr/math/vol44/iss2/6