扰动广义Liénard方程周期解的存在性
On the existence of periodic solution of perturbed generalized Liénard equations
摘要：
在Levinson-Smith型条件下，证明了具有周期强迫项的扰动广义Liénard方程u ''+<$（u，u '）u'+<$（u）=εω（\frac{t} τ，u，u '）的$τ$ -周期解的存在性.并给出了方程u“+ \sum_{k=0}^{2s+1} p_k（u）{u '}^k=εω（\frac{t} τ，u，u'）周期解存在的充分条件.我们的方法也可应用于方程u“+[u^2+（u+ u '）^2-1] u'+ u=εω（\frac{t} τ，u，u '）.数值例子说明了所得结果。
英文摘要：
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(\frac{t}τ,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=εω(\frac{t}τ,u,u'). Our method can be applied also to the equation u''+[u^2+(u+u')^2-1]u'+u=εω(\frac{t}τ,u,u'). The results obtained are illustrated with numerical examples.
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