Periodic solutions of \((2n+1)\)th order ordinary differential equations
type: Item
instance of: scholarly article
title: Periodic solutions of \((2n+1)\)th order ordinary differential equations
zbMATH Open document ID: 1017.34044
DOI: 10.1016/S0022-247X(02)00160-9
author: Guimei Jiao
published in: Journal of Mathematical Analysis and Applications
publication date: 2002-11-28T00:00:00Z
review text: The author uses the Leray-Schauder degree theory to prove that the equation \[ x^{(2n+1)}+f(t,x,x',...,x^{(2n)})=0 \] has a unique \(2\pi\)-periodic solution provided that \(f\) is \(C^1\), \(2\pi\)-periodic in time and the following conditions hold: (H1) \(|f(t,x)-f(t,y)|\leq \sum_{i=0}^{2n} c_{i} |x_{i}-y_{i}|\) for some \(c_0>0\) and \(c_i\geq 0\), (H2) there exists \(m>0\) such that \(m\leq |f_{x_{0}}|\leq c_{0}\) on \(\mathbb{R}\times \mathbb{R}^{2n+1}\) and \[ \left({c_{0} \over m} +1\right) \sum_{i=1}^{2n} (2\pi)^{2n-i+1} c_{i}<1. \]
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 1836790
zbMATH Keywords: periodic solutions
zbMATH Keywords: Leray-Schauder degree
zbMATH Keywords: (2n+1)th-order differential equation
reviewed by: Klaudiusz Wójcik
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1836790