Boundary-Value Problems for Differential-Difference Equations with Finite and Infinite Orbits of Boundaries

We consider boundary-value problems for differential-difference equations containing incommensurable shifts of arguments in the higher-order terms. We show that for the case where the orbits of the domain boundary generated by the set of shifts of the difference operator are finite, the original problem is similar to the boundary-value problem for differential-difference equations with integer shifts of arguments. The case of an infinite boundary orbit is also studied.