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Zbl 0689.34032
Gupta, Chaitan P.; Nieto, Juan J.; Sanchez, Luis
Periodic solutions of some Lienard and Duffing equations. (English)
[J] J. Math. Anal. Appl. 140, No.1, 67-82 (1989). ISSN 0022-247X

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 ${\bbfR}$ 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.
[S.G.Zhuravlev]

MSC 2000:: *34C25 Periodic solutions of ODE
34G10 Linear ODE in abstract spaces

Keywords: Caratheodory function

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