Journal of Applied Mathematics and Stochastic Analysis 
Volume 9 (1996), Issue 4, Pages 459-468
doi:10.1155/S1048953396000408

Differential inequalities for hysteresis systems

Vladimir V. Chernorutskii and Mark A. Krasnosel'skii

 Institute for Information Transmission Problems of RAS, 19, Bol'shoi Karetnyi pereulok, Moscow 101447, Russia
Received 1 April 1996; Revised 1 August 1996

Abstract

The theory of differential inequalities is extended to functional-differential equations with hysteresis nonlinearities. A key feature is the existence of a semiorder of the state space of nonlinearity and a special monotonicity of the righthand side of differential inequality.

This article is dedicated to the memory of Roland L. Dobrushin.