Direct and inverse nodal problem for differential pencil with coupled boundary conditions

Abstract

We consider the eigenvalue problem and inverse nodal problem for the s-wave Schrödinger equation with a radial static potential q(x) + 2λp(x) and with coupled boundary conditions on a finite segment. First, we establish an identity for the first regularized trace of this operator. Second, we prove that a dense subset of nodal points uniquely determines the parameters in the boundary conditions and the potential functions p(x) and q(x). We also provide a constructive procedure for the solution of the inverse nodal problem.