A nonlinear periodic averanging principle


This paper is devoted to a nonlinear averaging principle for periodic solutions of a class of second order inclusions. In addition an existence theorem for periodic solutions of such inclusions is established. This work which complements the abstract nonlinear averaging principle worked out in Couchouron and Kamenski (Nonlin. Anal. 42 (2000) 1101) makes a synthesis of the methods contained in Couchouron and Kamenski and Couchouron and Precup (Electron. J. Differential, Equations 4 (2002) 1) and represents a (nonvariational) topological approach for boundary values problems.


Jean-Francois Couchourn
Université de Metz, Mathématiques INRIA Lorraine, Ile du Saulcy, 57045 Metz, France

Mihail Kamenski
University of Voronezh, Faculty of Mathematics, 394693 Voronezh, Russia

Radu Precup
Department of Mathematics Babes-Bolyai University, Cluj-Napoca, Romania


Periodic solution; Averaging principle; Evolution equation; Dissipative operator, Multivalued mapping, Acyclic set, Fredholm inclusion; Fixed point

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J.-F. Couchouron, M. Kamenski, R. Precup,  A nonlinear periodic averanging principle,  Nonlinear Anal. 54 (2003), 1439-1467, https://doi.org/10.1016/S0362-546X(03)00196-2


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Nonlinear Analysis Theory Methods&Applications

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MR 1997229, Zbl 1034.34074.

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