Almost-periodic solutions to weakly nonlinear equations in critical cases
type: Item
instance of: scholarly article
title: Almost-periodic solutions to weakly nonlinear equations in critical cases
zbMATH Open document ID: 0982.34040
published in: Doklady Mathematics
publication date: 2001-01-28T00:00:00Z
review text: Consider the differential system \((*)\) \(dz/dt=Az+f(t)+\varepsilon Z(z,t,\varepsilon)\) under the assumptions (i) \(\varepsilon \) is a small parameter; (ii) \(A\) is a constant \(n \times n\)-matrix whose spectrum intersects the imaginary axis; (iii) \(f\) is quasi-periodic and can be represented as a Fourier series; (iv) \(Z\) is sufficiently smooth and quasi-periodic in \(t\). The author derives conditions on \(f\) and \(F\) guaranteeing the existence of an \(r\)-parametric family of quasi-periodic solutions to \((*)\) in case \(\varepsilon =0\) and the existence of a unique quasi-periodic solution to \((*)\) with \(\varepsilon\) sufficiently small, respectively.
Mathematics Subject Classification ID: 34C27
Mathematics Subject Classification ID: 34E10
zbMATH DE Number: 1557304
zbMATH Keywords: quasi-periodic solution
zbMATH Keywords: critical case
zbMATH Keywords: weakly nonlinear
author: S. M. Chujko
reviewed by: Klaus R. Schneider
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1557304