Journal of Applied Mathematics and Stochastic Analysis
Volume 9 (1996), Issue 4, Pages 459-468

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

Copyright © 1996 Vladimir V. Chernorutskii and Mark A. Krasnosel'skii. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.