Continuous dependence of solutions of boundary-value problems for differential-difference equations on shifts of the argument

We consider boundary-value problems for differential-difference operators with perturbations in shifts of the argument. We prove that the family of differential-difference operators is positive definite uniformly with respect to the shifts of the argument. Solutions of such problems depend continuously on these shifts. We consider the coercivity problem for differential-difference operators with incommensurable shifts of the argument and study the approximation of such operators by rational operators.