Existence of periodic solution for perturbed generalized Lienard equations

Electronic Journal of Differential Equations

关键词: Perturbed systems;    Lienard equation;    periodic solution.;   

DOI  :  

来源: DOAJ

【 摘 要 】

Under conditions of Levinson-Smith type, we prove the existence of a $au$-periodic solution for the perturbed generalized Li'enard equation $$ u''+varphi(u,u')u'+psi(u)=epsilonomega(frac{t}{au},u,u') $$ with periodic forcing term. Also we deduce sufficient condition for existence of a periodic solution for the equation $$ u''+sum_{k=0}^{2s+1} p_k(u){u'}^k=epsilonomega(frac{t}{au},u,u'). $$ Our method can be applied also to the equation $$ u''+[u^2+(u+u')^2-1]u'+u=epsilonomega(frac{t}{au},u,u'). $$ The results obtained are illustrated with numerical examples.

【 授权许可】

Unknown