Existence of closed solutions for a polynomial first order differential equation
type: Item
instance of: scholarly article
title: Existence of closed solutions for a polynomial first order differential equation
zbMATH Open document ID: 1115.34038
author: Pedro J. Torres
published in: Journal of Mathematical Analysis and Applications
publication date: 2007-02-12T00:00:00Z
review text: Consider the scalar differential equation \[ \frac{dx}{dt}= \sum^n_{k=0}a_k(t)x^k, \tag{*} \] where \(a_k\in C([0,2\pi])\), \(k=0, \dots,n\), \(n\geq 2\). Assuming \(\int^{2 \pi}_0a_1 (t)dt\neq 0,\) the author derives conditions for (*) to have at least one solution satisfying \(x(0)= x(2\pi)\). He applies his result to planar polynomial vector fields to get criteria for the existence of at least one limit cycle.
reviewed by: Klaus R. Schneider
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34C05
zbMATH DE Number: 5124017
zbMATH Keywords: abel equation
zbMATH Keywords: closed solution
zbMATH Keywords: limit cycle
zbMATH Keywords: planar polynomial vector field
Wikidata QID: Q115346269
MaRDI profile type: Publication
full work available at URL: j.jmaa.2006.05.078
OpenAlex ID: W2091050507
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DOI: 10.1016/J.JMAA.2006.05.078
description: scientific article; zbMATH DE number 5124017