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


34C25 Periodic solutions to ordinary differential equations
34G10 Linear differential equations in abstract spaces
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