On a boundedness condition for solutions of a generalized Liénard equation
type: Item
instance of: scholarly article
title: On a boundedness condition for solutions of a generalized Liénard equation
zbMATH Open document ID: 0612.34042
DOI: 10.1016/0022-0396(86)90038-0
author: Junji Kato
published in: Journal of Differential Equations
publication date: 1986-01-01T00:00:00Z
review text: A Liénard type system \[ (1)\quad x'=y-f(x)+p(t),\quad y'=-g(x) \] is considered, where f,g are locally Lipschitz continuous in \({\mathbb{R}}\) and p is bounded and piecewise absolutely continuous in [0,\(\infty)\). The main theorems give conditions on f,g,p for the solutions of (1) to be uniformly bounded, uniformly ultimately bounded, or unbounded. Also a uniform boundedness theorem is obtained for a vector analogue of (1).
reviewed by: Charles A. Swanson
Mathematics Subject Classification ID: 34D05
Mathematics Subject Classification ID: 34C11
Mathematics Subject Classification ID: 34D40
zbMATH DE Number: 3989831
zbMATH Keywords: Liénard equation
zbMATH Keywords: unbounded solution
zbMATH Keywords: first order differential equation
zbMATH Keywords: uniform boundedness theorem
MaRDI profile type: Publication
full work available at URL: 0022-0396(86)90038-0
OpenAlex ID: W1992964077
cites work: Q5736289
cites work: Asymptotic directions for solutions of Liénard systems
cites work: Second order boundedness criteria
cites work: On the generalized Lienard equation with forcing function
cites work: On the Boundedness of Solutions of Classes of Multidimensional Nonlinear Autonomous Systems
cites work: Q3660126
cites work: On the generalized Lienard equation with negative damping
cites work: Necessary and Sufficient Conditions for the Continuability of Solutions of the System
cites work: Q3247296
cites work: An extension of a theorem of A. C. Lazer on forced nonlinear oscillations
cites work: Expension of some results concerning the generalized Lienard equation
cites work: Q4777660
cites work: Q5335550
cites work: Q5182535
cites work: Periodic solutions of Lienard's equation
cites work: Q3969220
cites work: Q5520199
cites work: Q3952431
Recommended article: Q3368885
Recommended article: Boundedness and stability properties of solutions of generalized Liénard equations
Recommended article: Q4272966
Recommended article: On the boundedness of solutions of the generalized Liénard equation without the signum condition
Recommended article: Q5319075
Recommended article: Q4387568
Recommended article: Boundedness of solutions for a class of Liénard equations with a deviating argument
Recommended article: Q4501373
Recommended article: Q4856899
Recommended article: Boundedness of solutions for a class of Liénard equation with multiple deviating arguments
description: scientific article; zbMATH DE number 3989831