Continuous Dependence of Solutions of Boundary-Value Problems for Di erential-Di erence Equations on Shifts of the Argument

Abstract

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