Existence of periodic solutions with nonconstant sign in a class of generalized Abel equations
type: Item
instance of: scholarly article
title: Existence of periodic solutions with nonconstant sign in a class of generalized Abel equations
zbMATH Open document ID: 1277.34038
author: Josep M. Olm
author: Xavier Ros-Oton
published in: Discrete and Continuous Dynamical Systems
publication date: 2013-04-24T00:00:00Z
review text: The authors consider the differential equation \[ x^{m} \dot{x}=\sum_{k=0}^{n} a_{k}(t)x^{k}, \] where \(a_{k}\) are continuous \(T\)-periodic functions and \(m\) is a non-negative integer. It is assumed also that \(a_{0}(t)\) has at least one zero in the interval \((0,T)\). It is shown that the equation has a \(T\)-periodic solution which has the sign of \((-1)^{m}a_{0}(t)\) if some conditions on the other coefficients are satisfied.
reviewed by: M. A. M. Alwash
Mathematics Subject Classification ID: 34C07
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 6157269
zbMATH Keywords: Abel differential equation
zbMATH Keywords: limit cycles
zbMATH Keywords: polynomial differential systems
zbMATH Keywords: Hilbert's 16th problem
MaRDI profile type: Publication
full work available at URL: dcds.2013.33.1603
OpenAlex ID: W2323433113
DOI: 10.3934/DCDS.2013.33.1603
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description: scientific article; zbMATH DE number 6157269