Inverse nodal problems for the Sturm-Liouville operator with eigenparameter dependent boundary conditions

Abstract

An inverse nodal problem consists in reconstructing this operator from the given zeros of their eigenfunctions. In this work, we are concerned with the inverse nodal problem of the Sturm-Liouville operator with eigenparameter dependent boundary conditions on a finite interval. We prove uniqueness theorems: a dense subset of nodal points uniquely determine the parameters of the boundary conditions and the potential function of the Sturm-Liouville equation; and provide a constructive procedure for the solution of the inverse nodal problems. Mathematics subject classification (2010): 47A10, 47A20, 47A45, 47A67, 47B25.