Classical solutions of boundary value problems for differential-difference equations

For a differential-difference equation of the second order on the interval [0, d], we study the existence of a classical solution for arbitrary continuous right-hand sides. We show that a necessary and sufficient condition for the existence of a classical solution of the problem in the case where there exists a generalized solution is the absence of argument shifts in the derivatives of the unknown function occurring in the equation. © 2013 Pleiades Publishing, Ltd