Periodic solutions of second-order nonlinear difference equations containing a small parameter. II: Equivalent linearization
type: Item
instance of: scholarly article
title: Periodic solutions of second-order nonlinear difference equations containing a small parameter. II: Equivalent linearization
zbMATH Open document ID: 0589.39004
DOI: 10.1016/0016-0032(85)90043-2
author: Ronald E. Mickens
published in: Journal of the Franklin Institute
publication date: 1985-01-01T00:00:00Z
review text: [For part I see ibid. 316, 273-277 (1983; Zbl 0529.39002).] The classical method of equivalent linearization is applied to obtain approximations to the periodic solutions of the following class of nonlinear difference equations \[ x_{k+1}-(2 \cos \phi)x_ k+x_{k- 1}=\epsilon f(x_ k,x_{k-1}) \] where \(k=0,1,2,...\); \(\phi\) is a given constant; f is a polynomial function of its arguments and \(0<\epsilon \ll 1\) is a small positive parameter.
Mathematics Subject Classification ID: 39A10
zbMATH DE Number: 3946794
zbMATH Keywords: method of equivalent linearization
zbMATH Keywords: periodic solutions
zbMATH Keywords: nonlinear difference equations
reviewed by: Vinicio C. Boffi
MaRDI profile type: Publication
full work available at URL: 0016-0032(85)90043-2
OpenAlex ID: W2003251688
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description: scientific article; zbMATH DE number 3946794