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 ].
Mathematics Subject Classification:
Acknowledgments
This work is supported by the National Natural Science Foundation of China (no. 61573004) and also in part supported by Promotion Program for Young and Middle-aged Teacher in Science and Technology Research of Huaqiao University (ZQN-YX301), the Natural Science Foundation of Fujian Province (2015J01260) and the Program for New Century Excellent Talents in Fujian Province University. Authors would also like to thank the reviewers for their careful work.
Disclosure statement
No potential conflict of interest was reported by the authors.