Multiplicity of periodic solutions for the planar polynomial equation
type: Item
instance of: scholarly article
title: Multiplicity of periodic solutions for the planar polynomial equation
zbMATH Open document ID: 1008.34034
DOI: 10.1016/S0362-546X(99)00191-1
author: Andrei Borisovich
author: Wacław Marzantowicz
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2003-03-25T00:00:00Z
review text: Here, the authors study the existence and multiplicity of periodic solutions to the following planar polynomial equation \(\dot z = \sum_{j=0}^nc_j(t)z^j\), where \(c_j\) are periodic functions. Based on Leray-Schauder degree, they prove that this equation has at least \(s\) distinct periodic solutions if the polynomial \(\sum_{j=0}^n{\bar c_j(t)}z^j\) has \(s\) distinct roots, where \(\bar c_j(t)\) is the average of \(c_j(t)\).
reviewed by: Bin Liu
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 1545352
zbMATH Keywords: periodic solutions
zbMATH Keywords: planar ordinary differential equation
zbMATH Keywords: a priori estimate
MaRDI profile type: Publication
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full work available at URL: s0362-546x(99)00191-1
OpenAlex ID: W1983556355
description: scientific article; zbMATH DE number 1545352