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

In this paper, we consider a boundary value problem withaftereffect on a finite interval. then, the asymptotic behavior of thesolutions, eigenvalues, the nodal points and the associated nodal lengthare studied. we also calculate the numerical values of the nodal pointsand the nodal length. finally, we prove the uniqueness theorem for theinverse aftereffect problem by applying any dense subset of the nodalpoints.