On spectral properties of a fourth-order boundary value problem with impulse

Abstract

In this paper, we consider a fourth-order boundary value problem with impulse. We apply the Fourier method for solving of this problem arising in finding of transverse vibration of a string. We calculate the eigenvalues and eigenfunctions of the fourth-order boundary value problem for some ordinary differential equation with piecewise constant coefficient. We obtain a solution of the considered equation subject to initial data, boundary and transmission conditions at the point of discontinuity.