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On periodic solutions of second order ordinary differential equations not in explicit form with respect to the derivative. (Russian) Zbl 0604.34023

Consider the system of differential equations in vector form (1) \(\ddot x=A(t)x+f(t,x,\dot x,\ddot x),\) \(x\in R^ n\), A(t) is a continuous \(n\times n\) matrix \(\omega\)-periodic in t, f is continuous in its arguments, \(\omega\)-periodic in t, and satisfies Lipschitz conditions. The author proves that under certain conditions the system (1) has a unique \(\omega\)-periodic solution and presents a scheme for its construction.
Reviewer: G.Bojadziev

MSC:

34C25 Periodic solutions to ordinary differential equations
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