Boundary-Value Problems for Differential-Difference Equations with Incommeasurable Shifts of Arguments Reducible to Nonlocal Problems

Abstract

We consider boundary-value problems for differential-difference equations containing incommeasurable shifts of arguments in higher-order terms. We prove that in the case of finite orbits of boundary points generated by the set of shifts of the difference operator, the original problem is reduced to the boundary-value problem for differential equation with nonlocal boundary conditions.