The uniqueness theorem for discontinuous boundary value problems with aftereffect using the nodal points

Abstract

In this paper, uniqueness theorem is studied for boundary value problem with "aftereffect" on a finite interval with discontinuity conditions in an interior point. The oscillation of the eigenfunctions corresponding to large modulus eigenvalues is established and an asymptotic of the nodal points is obtained. By using these new spectral parameters, uniqueness theorem is proved.