The second boundary value problem for differential-difference equations with variable coefficients on an interval of integer length

The second boundary value problem for a second-order differential-difference equation with variable coefficients on an interval of non-integer length is considered. The existence of a generalized solution of the problem is proved. We prove the smoothness of generalized solutions over the entire interval of non-integer length in case the right-hand side of the differential-difference equation is orthogonal in the space $L_2 (0,d)$, $d\notin N$, to a finite number of linearly independent functions is fulfilled.
This is a joint work with Alexander L. Skubachevskii.