On Generalized Solutions of the First Boundary Value Problem for Differential-Difference Equations with Variable Coefficients

Abstract We consider the first boundary value problem for a second-order differential-difference equation with variable coefficients on the interval $$(0,d)$$ . The existence of a generalized solution is proved. We investigated the smoothness of generalized solutions on $$(0,d)$$ and explicitly obtained linearly independent functions to which the right-hand side of the differential-difference equation must be orthogonal.