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Periodic solutions of nonlinear periodic differential systems with a small parameter

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  • We deal with nonlinear periodic differential systems depending on a small parameter. The unperturbed system has an invariant manifold of periodic solutions. We provide sufficient conditions in order that some of the periodic orbits of this invariant manifold persist after the perturbation. These conditions are not difficult to check, as we show in some applications. The key tool for proving the main result is the Lyapunov--Schmidt reduction method applied to the Poincaré--Andronov mapping.
    Mathematics Subject Classification: Primary: 34C29, 34C25; Secondary: 58F22.


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