Boundary-value problems for differential-difference equations with nite and in nite orbits of boundaries

Abstract

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 when the orbits of the domain boundary generated by the set of shifts of the difference operator are nite, the original problem is similar to the boundary-value problem for differential-difference equations with integer shifts of arguments. The case of an in nite boundary orbit is also studied.