On the existence of periodic solutions for certain differential equations
type: Item
instance of: scholarly article
title: On the existence of periodic solutions for certain differential equations
zbMATH Open document ID: 1069.34064
published in: Journal of Computational and Applied Mathematics
publication date: 2005-02-23T00:00:00Z
review text: The paper is concerned with the existence of periodic solutions for two classes of second- and third-order nonlinear differential equations. By means of topological degree theory, it is established that if under certain conditions, the differential equation \[ x^{\prime\prime}+\lambda\phi(t)f(x)h(x^{\prime})=0 \] has a periodic solution, then there exists a periodic solution of \[ x^{\prime\prime}+\lambda_{\sigma}\phi(t)g(x,x^{\prime},\sigma)=0. \] A similar result is proved also for the third-order nonlinear differential equation \[ x^{\prime\prime\prime}+\lambda\phi(t)g(x,x^{\prime},x^{\prime\prime} ,\sigma)=0. \] The paper concludes with illustrative examples.
reviewed by: Svitlana P. Rogovchenko
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47H11
zbMATH DE Number: 2137429
zbMATH Keywords: periodic solutions
zbMATH Keywords: existence
zbMATH Keywords: Schauder degree
zbMATH Keywords: Green's function
zbMATH Keywords: eigenvalue problem
author: Bahman Mehri
author: M. Niksirat
MaRDI profile type: Publication
full work available at URL: j.cam.2004.04.011
OpenAlex ID: W4239531989
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cites work: On Schauder's fixed point theorem and forced second-order nonlinear oscillations
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DOI: 10.1016/J.CAM.2004.04.011
description: scientific article; zbMATH DE number 2137429