Inverse Nodal Problem for Polynomial Potentials

Abstract

In this work, we study an inverse nodal problem for a differential pencil with boundary condition depends on eigenparameter. We show that there exists a solution of the problem that satisfied the conditions. Also, we give eigenvalues, nodal points and some formulas for qn(x). Although there were given some results for this type problem, we think that inverse nodal problems have not solved yet.