Small parameter perturbations of nonlinear periodic systems

Details Small parameter perturbations of nonlinear periodic systems Small parameter perturbations of nonlinear periodic systems

2007-09-29

arxiv.org/abs/0710.0056v1

Nonlinearity, 17 (2004) 193-205

Mathematics

Classical Analysis and ODEs

Scientific paper

10.1088/0951-7715/17/1/012

In this paper we consider a class of nonlinear periodic differential systems perturbed by two nonlinear periodic terms with multiplicative different powers of a small parameter $e>0$. For such a class of systems we provide conditions which guarantee the existence of periodic solutions of given period $T>0$. These conditions are expressed in terms of the behaviour on the boundary of an open bounded set $U$ of $R^n$ of the solutions of suitably defined linearized systems. The approach is based on the classical theory of the topological degree for compact vector fields. An application to the existence of periodic solutions to the van der Pol equation is also presented.

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