On the existence of solutions for strongly nonlinear differential equations
type: Item
instance of: scholarly article
title: On the existence of solutions for strongly nonlinear differential equations
zbMATH Open document ID: 1160.34002
author: Kamel Al-Khaled
author: M. A. Hajji
published in: Journal of Mathematical Analysis and Applications
publication date: 2008-06-17T00:00:00Z
review text: The objective of this paper is to find approximate solutions to the differential equation \[ \ddot{x}(t)+a{\dot{x}}^2(t)+bx(t)=F(t). \] The authors prove that if \(F\) is a bounded, odd periodic function, then under suitable conditions on it and its derivative, there exists a solution in the mean of the differential equation which is computable. The paper contains also a discussion on the homotopy perturbation method applied to the construction of analytic solutions of the differential equation but it does not contain results on the converge of the method.
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 34A05
Mathematics Subject Classification ID: 34A45
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 5289218
zbMATH Keywords: non linear differential equation
zbMATH Keywords: solution in the mean
zbMATH Keywords: homotopy perturbation method
reviewed by: Rosa Maria Bianchini
MaRDI profile type: Publication
full work available at URL: j.jmaa.2008.03.022
OpenAlex ID: W2093209717
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DOI: 10.1016/J.JMAA.2008.03.022
description: scientific article; zbMATH DE number 5289218