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Asymptotic Equivalence of Evolution Equations Governed by Cocoercive Operators and Their Forward Discretizations
(Springer New York LLC, 2019)
© 2018, Springer Science+Business Media, LLC, part of Springer Nature.The purpose of this work is to study discrete approximations of evolution equations governed by cocoercive operators by means of Euler iterations, both ...
Dichotomies and asymptotic equivalence in alternately advanced and delayed differential systems
(Academic Press, 2017)
In this paper, ordinary and exponential dichotomies are defined in differential equations with equations with piecewise constant argument of general type. We prove the asymptotic equivalence between the bounded solutions ...
Asymptotic properties of solutions to nonautonomous Volterra difference systems with infinite delay
(2001)
We show that under certain conditions there is a one-to-one correspondence between weighted bounded solutions of a linear nonautonomous Volterra difference system with infinite delay and its perturbed system. Under additional ...
(h, k)-Trichotomies and asymptotics of nonautonomous difference systems
(Elsevier Ltd, 1997)
Discrete nonautonomous nonlinear systems possessing (h, k)-trichotomies are considered. We specialize to the case of solutions moving inside - and in a neighborhood of - an invariant manifold of a special kind, which we ...
Smoothness of topological equivalence on the half line for nonautonomous systems
(Cambridge University Press, 2020)
We study the differentiability properties of the topological equivalence between a uniformly asymptotically stable linear nonautonomous system and a perturbed system with suitable nonlinearities. For this purpose, we ...
Null solutions of difference systems under vanishing perturbation
(2003)
For difference systems, the new concept expo-(h,k) dichotomy is introduced and exhaustively studied for being used in the asymptotic equivalence of null solutions. An application to Poincaré equations is shown.
Smoothness of topological equivalence on the half line for nonautonomous systems.
(Cambridge University Press, 2019)
We study the differentiability properties of the topological equivalence between a uniformly asymptotically stable linear nonautonomous system and a perturbed system with suitable nonlinearities. For this purpose, we ...
A unified approach to the asymptotic almost-equivalence of evolution systems without Lipschitz conditions
(PERGAMON-ELSEVIER SCIENCE LTD, 2011)