Existence of periodic solutions for a class of second order ordinary differential equations
type: Item
instance of: scholarly article
title: Existence of periodic solutions for a class of second order ordinary differential equations
zbMATH Open document ID: 1494.34119
author: Jaume Llibre
author: Antonio García
published in: Acta Applicandae Mathematicae
publication date: 2021-05-03T00:00:00Z
full work available at URL: http://ddd.uab.cat/record/228090
review text: This paper studies the existence of a \(2\pi-\)periodic solution to the equation \[ \ddot{x}+g(x)=\mu^{2n+1}p(t)+\mu^{4n+1}q(t,x,\dot{x},\mu), \] where \(n\) is a positive integer, \(\mu\) is a small parameter, the functions \(p\) and \(q(t,x,y,\mu)\) are smooth with period \(2\pi\) in the variable \(t\), and \[ g(x)=x+x^{2n+1}(b+xh(x)), \] where \(b\neq 0\) and \(h(x)\) is smooth too. After doing a re-scaling in the variables \((x,\dot{x})\), an approximation procedure for periodic solutions via averaging method is applied to solve the problem.
reviewed by: Manuel Zamora
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34C29
Mathematics Subject Classification ID: 34E10
Mathematics Subject Classification ID: 37C60
zbMATH DE Number: 7341768
zbMATH Keywords: periodic solution
zbMATH Keywords: second-order differential equation
zbMATH Keywords: averaging theory
MaRDI profile type: Publication
OpenAlex ID: W2982008963
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DOI: 10.1007/S10440-019-00295-9
description: scientific article; zbMATH DE number 7341768