Asymptotic behavior of solutions to a class of differential equations in infinite-dimensional spaces
type: Item
instance of: scholarly article
title: Asymptotic behavior of solutions to a class of differential equations in infinite-dimensional spaces
zbMATH Open document ID: 0944.34051
DOI: 10.1016/S0362-546X(98)00167-9
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2000-09-04T00:00:00Z
review text: The author considers the asymptotic behavior of solutions to a coupled system of two nonlinear evolution equations of the form \[ \dot{x} = A(t)x + f(t,x,y), \quad x(t_0) = x_0, \] \[ \dot{y} = B(t)x + g(t,x,y), \quad y(t_0) = y_0, \] for \((x,y) \in X \times X\), \(X\) a Banach space. The existence of \(\delta\)-bounded solutions is studied, i.e., \((x(t),y(t))\) satisfies \[ \||x(t)\||\leq \delta_1(t), \quad \||y(t)\||\leq \delta_2(t), \] with nonnegative scalar functions \(\delta_i\). Criteria for the existence of such solutions are given and applied to functional-differential equations and infinite-dimensional systems of ordinary differential equations.
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 34D05
Mathematics Subject Classification ID: 34K05
Mathematics Subject Classification ID: 34A35
zbMATH DE Number: 1389528
zbMATH Keywords: asymptotic behavior
zbMATH Keywords: infinite-dimensional spaces
zbMATH Keywords: topological method
zbMATH Keywords: functional-differential equation
author: A. F. Izé
reviewed by: S. Siegmund
MaRDI profile type: Publication
full work available at URL: s0362-546x(98)00167-9
OpenAlex ID: W2035687913
description: scientific article; zbMATH DE number 1389528