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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 386812, 9 pages
http://dx.doi.org/10.1155/2013/386812
Research Article

Reducibility for a Class of Almost-Periodic Differential Equations with Degenerate Equilibrium Point under Small Almost-Periodic Perturbations

1School of Mathematics, Shandong University, Jinan, Shandong 250100, China
2School of Mathematics and Statistics, Zaozhuang University, Zaozhuang, Shandong 277160, China

Received 18 July 2013; Revised 10 October 2013; Accepted 13 October 2013

Academic Editor: Svatoslav Staněk

Copyright © 2013 Wenhua Qiu and Jianguo Si. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper focuses on almost-periodic time-dependent perturbations of an almost-periodic differential equation near the degenerate equilibrium point. Using the KAM method, the perturbed equation can be reduced to a suitable normal form with zero as equilibrium point by an affine almost-periodic transformation. Hence, for the equation we can obtain a small almost-periodic solution.