Existence of periodic solutions of a ordinary differential equation perturbed by a small parameter: An averaging approach |
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| Authors: | Anastasia Gudovich Mikhail Kamenskii Marc Quincampoix |
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| Institution: | 1. Department of Applied Mathematics and Mechanics, Voronezh State University, 1 Universitetskaya pl., 394006 Voronezh, Russia;2. Department of Mathematics, Voronezh State University, 1 Universitetskaya pl., 394006 Voronezh, Russia;3. Laboratoire de mathématiques, UMR CNRS 6205, Université de Bretagne Occidentale, 6, avenue Victor-Le-Gorgeu, 29200 Brest, France |
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| Abstract: | In this Note, we obtain two new results for existence of periodic solutions for differential equations perturbed by a small parameter. The first one is based on a new fixed point theorem previously obtained by the authors. The second one is based on study of suitable linearized equations. Our approach deals with degree theory and nonsmooth analysis. To cite this article: A. Gudovich et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009). |
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