Lipschitz Generalization of Malkin-loud Result on the Existence and Uniqueness of Periodic Solutions
نویسندگان
چکیده
We consider a system of differential equations possessing a family of T -periodic solutions and subjected to a T -periodic Lipschitz small perturbation. We prove the existence and uniqueness of a T -periodic solution of the perturbed system by means of a Lipschitz generalization of the Lyapunov–Schmidt reduction method. When the perturbation is continuously differentiable our result coincides with the existence and uniqueness part of the classical result of Malkin. An application of the main result is also provided.
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