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On the reducibility of a nonlinear periodic system with degenerate equilibrium

ABSTRACT In this paper, we prove the reducibility of a class of nonlinear periodic differential equation with degenerate equilibrium point under small perturbations, and obtain a periodic solution near the equilibrium point. The result is new and more general, including that of the paper [X. Lu and J. Xu, On small perturbations of a nonlinear periodic system with degenerate equilibrium, Nonlinear Differ. Equ. Appl. 21 (2014), pp. 361–370 ].