Uniqueness Theorem for the Inverse Aftereffect Problem and Representation the Nodal Points Form

In this paper, we consider a boundary value problem with aftereffect on a finite interval. Then, the asymptotic behavior of the solutions, eigenvalues, the nodal points and the associated nodal length are studied. We also calculate the numerical values of the nodal points and the nodal length. Finally, we prove the uniqueness theorem for the inverse aftereffect problem by applying any dense subset of the nodal points.