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 $q_n(x).$ Although there were given some results for this type problem, we think that inverse nodal problems have not solved yet.

Keywords:

• Polynomial potentials
• nodal inverse problem
• nodes of eigenfunctions

2000 MATHEMATICS SUBJECT CLASSIFICATION:

• 34A55
• 34B24
• 34L20
• 34L30