Maximum principles for linear difference-differential operators in periodic function spaces

Summary

Given a difference-differential equation of the type

$$u^{\left( n \right)} \left( t \right) + au\left( t \right) + bu\left( {t - \tau } \right) = f\left( t \right), n = 1, 2$$

inT-periodic function spaces, we find conditions on the constantsa,b, τ,T which are necessary and sufficient for the validity of maximum and minimum principles. The theoretical results are completed by a numerical procedure for the actual computation of such conditions.