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Periodic solutions of some Lienard and Duffing equations. (English) Zbl 0689.34032
The problem of existence of periodical solutions of differential equations of the form $(1)\quad u''+f(u)u'+g(t,u)=0,\quad u(0)=u(2\pi),\quad u'=u'(2\pi),$ where f(u) is a continuous function on $${\mathbb{R}}$$ and g(t,u) is a Caratheodory function subject to certain growth restrictions, is considered. Several existence theorems providing the periodic solutions of (1) in resonance and some other particular cases (i.e. for $$f(u)=const$$, f(u)$$\equiv 0$$ etc.) are proved.
Reviewer: S.G.Zhuravlev

##### MSC:
 34C25 Periodic solutions to ordinary differential equations 34G10 Linear differential equations in abstract spaces
##### Keywords:
Caratheodory function
Full Text:
##### References:
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