Zdzisław Kamont, Adam Nadolski

Functional Differential Inequalities with Unbounded Delay

We prove that a function of several variables satisfying a functional differential inequality with unbounded delay can be estimated by a solution of a suitable initial problem for an ordinary functional differential equation. As a consequence of the comparison theorem we obtain a Perron-type uniqueness result and a result on continuous dependence of solutions on given functions for partial functional differential equations with unbounded delay. We consider classical solutions on the Haar pyramid.

Maximal solutions, initial problems, unbounded delay, nonlinear estimates of the Perron type, comparison result.

MSC 2000: 35R10, 34K12