Journal of Applied Mathematics and Stochastic Analysis
Volume 3 (1990), Issue 2, Pages 85-97

On the theory of one-sided models in spaces with arbitrary cones

A. A. Martynyuk and A. Yu. Obolensky

Institute of Mechanics, The Ukrainian Academy of Sciences, Nesterov Str. 3, Kiev-57 252057, Russia

Received 1 September 1989; Revised 1 November 1989

Copyright © 1990 A. A. Martynyuk and A. Yu. Obolensky. 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 paper presents a way of constructing quasimonotone nonautonomous systems ensuring x-stability of the nonautonomous system. There are described extensions quasimonotone with respect to an arbitrary cone, Perron condition and invariant surface stability under perturbations U-stability on the set of non wandering points is proved to imply u-stability of quasimonotone nonlinear system and exponential u-stability on minimal attraction center provides u-stability of the total systems Examples are available.