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An averaging result for periodic solutions of Carathéodory differential equations

This paper is concerned with the problem of existence of periodic solutions for perturbative Carathéodory differential equations. The main result provides sufficient conditions on the averaged equation that guarantee the existence of periodic solutions. Additional conditions are also provided to ensure the uniform convergence of a periodic solution to a constant function. The proof of the main theorem is mainly based on an abstract continuation result for operator equations.

preprint2022arXivOpen access
Douglas D. Novaes
math.DS
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Douglas D. Novaes

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