The qualitative behavior of a second-order system with zero diagonal coefficient.
type: Item
instance of: scholarly article
title: The qualitative behavior of a second-order system with zero diagonal coefficient.
zbMATH Open document ID: 1048.34065
author: Mats Gyllenberg
author: Ping Yan
author: Jifa Jiang
published in: Journal of Mathematical Analysis and Applications
publication date: 2004-03-14T00:00:00Z
review text: The authors investigate the qualitative behavior of solutions of the autonomous planar system \[ \dot{x}=p_2(y)\,q_2(x)\,y,\quad \dot{y}=p_3(y)\,q_3(x)\,x+p_4(y)\,q_4(x)\,y. \] Under suitable assumptions, necessary and sufficient conditions for all solutions to be oscillatory and for the origin to be a global center are established. Theorems on the existence and uniqueness of nontrivial periodic solutions are also proved.
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 2056515
zbMATH Keywords: second-order autonomous system
zbMATH Keywords: periodic solution
reviewed by: Valery A. Gaiko
MaRDI profile type: Publication
full work available at URL: j.jmaa.2003.11.006
OpenAlex ID: W2087506169
cites work: Q5811454
cites work: The generalized Liénard systems
cites work: When do all trajectories in the Liénard plane cross the vertical isocline?
cites work: Q3710853
cites work: A necessary and sufficient condition for oscillation of the generalized Liénard equation
cites work: Q3933274
cites work: Q4514429
cites work: Q4297917
cites work: Sopra l'equazione di A. Lienard delle oscillazioni di rilassamento
cites work: The global centre for the Liénard system
cites work: Q3356689
cites work: On Global Asymptotic Stability of Second Order Nonlinear Differential Systems
cites work: Q4004269
cites work: Q3715459
DOI: 10.1016/J.JMAA.2003.11.006
description: scientific article; zbMATH DE number 2056515