Zdzisław Kamont, Adam Nadolski

Functional Differential Inequalities with Unbounded Delay

Abstract:
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.

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

MSC 2000: 35R10, 34K12