Reconstruction of potential function and its derivatives for Sturm-Liouville problem with eigenvalues in boundary condition

Abstract

The purpose of this article is solving inverse nodal problem for Sturm-Liouville equation with a boundary condition depending on spectral parameter. Taking into account Law and Chen's method, we construct the potential function q and its derivatives by using nodal data. We give several lemmas in order to complete proof of the main theorem. Especially, we obtain an explicit formula for potential function and its derivatives from the nodal data by a pointwise limit.