On the existence of a limiting regime in the sense of Demidovic for a certain fourth-order nonlinear differential equation
type: Item
instance of: scholarly article
title: On the existence of a limiting regime in the sense of Demidovic for a certain fourth-order nonlinear differential equation
zbMATH Open document ID: 0654.34029
DOI: 10.1016/0022-247X(88)90258-2
published in: Journal of Mathematical Analysis and Applications
publication date: 1988-01-01T00:00:00Z
review text: A solution X(t) of the ordinary fourth order DE \[ (*)\quad x+a\dot{\ddot x}+b\ddot x+c\dot x+h(x)=p(t,x,\dot x,\ddot x\dot{\ddot x}), \] with a,b,c positive constants, h and p continuous, is said to be a Demidovic limit regime if \((X^ 2+\dot X^ 2+\ddot X^ 2+\dot{\ddot X}^ 2)^{1/2}\leq m\) for a finite m and all \(t\in {\mathbb{R}}\), and if every other solution converges to X as \(t\to \infty\). The author gives some sufficient conditions on h and p under which a limit regime exists and is periodic or almost periodic when p, as a function of t, has those properties.
Mathematics Subject Classification ID: 34C11
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34C27
zbMATH DE Number: 4067372
zbMATH Keywords: Demidovic limit regime
Wikidata QID: Q115364527
author: Anthony Uyi Afuwape
reviewed by: E. Brommundt
MaRDI profile type: Publication
cites work: Q3947964
cites work: On the existence of a limiting regime of a certain non-linear system of ordinary differential equations
cites work: Q5343627
cites work: Q5682659
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cites work: On the convergence of solutions of certain third-order differential equations
description: scientific article; zbMATH DE number 4067372