Continuous Dependence on Translations of the Independent Variable for Solutions of Boundary-Value Problems for Differential-Difference Equations

We consider boundary-value problems for differential-difference operators with perturbations in translations of the independent variable. We prove that the family of differential-difference operators is positive definite uniformly with respect to translations of the independent variable. Solutions of such problems depend continuously on these translations. We consider the coercivity problem for differential-difference operators with incommensurable translations of the independent variable and study the approximation of such operators by rational operators. © 2018, Springer Science+Business Media, LLC, part of Springer Nature.