On the existence of periodic solution of perturbed generalized Liénard equations

2006/10/27 by Islam Boussaada, Boussaada, Islam, A. Raouf Chouikha +1
Mathematics · #34C25 #Advanced Differential Equations and Dynamical Systems #Classical Analysis and ODEs (math.CA) #Differential Equations and Numerical Methods #FOS: Mathematics #Nonlinear Differential Equations Analysis #math.CA #msc:34C25

paper · pdf · doi:10.48550/arxiv.math/0610847

15 pages, 5 figures

arxiv created 2006/10/27 · openalex publication_date 2006/10/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Under conditions of Levinson-Smith type, we prove the existence of a τ-periodic solution for the perturbed generalized Liénard equation u''+ϕ(u,u')u'+ψ(u)=εω(\fractτ,u,u') with periodic forcing term. Also we deduce sufficient condition for existence of a periodic solution for the equation u''+∑_k=0^2s+1 p_k(u)u'^k=εω(\fractτ,u,u'). Our method can be applied also to the equation u''+[u²+(u+u')²-1]u'+u=εω(\fractτ,u,u'). The results obtained are illustrated with numerical examples.

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