Inverse nodal problem for discontinuous Sturm–Liouville operator by new Prüfer Substitutions

Abstract

In the present paper, a boundary value problem consisting of a Sturm–Liouville equation with boundary conditions dependent on the eigenparameter and discontinuous conditions inside the interval is investigated. We present new Prufer substitutions and obtain the asymptotic form of eigenvalues, nodal points and nodal lengths. Then, we prove the uniqueness theorem for the solution of the inverse nodal problem, present a constructive procedure for the potential function by using nodal lengths. Finally, we study Lipschitz stability for the inverse problem.