The inverse nodal problem for a differential operator with an eigenvalue in the boundary condition

Abstract

We consider the Sturm–Liouville problem with an eigenvalue dependent boundary condition. In this work, by using method of Yang [X.F. Yang, A solution of the inverse nodal problem, Inverse Problems 13 (1997) 203–213.], we reconstruct the potential of the Sturm–Liouville problem with an eigenvalue in the boundary condition from nodal points (zeros of eigenfunctions). Also, we give a uniqueness theorem.