The second boundary value problem for differential-difference equations

We consider the second boundary value problem for a second-order differential-difference equation with variable coefficients on the interval $(0,d)$. It was obtained the necessary and sufficient condition for the existence of a generalized solution. It was proved that, if the right-hand side of the equation is orthogonal in $L_2(0,d)$ to some functions, then a generalized solution from the Sobolev space $W^1_2(0,d)$ belongs to the space $W_2^2(0,d)$.