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 ].

Keywords:

• Periodic system
• reducibility
• degenerate equilibrium
• small perturbations

Mathematics Subject Classification:

• Primary 37J40
• Secondary 70H12
• 34C20

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.

Additional information

Funding

National Natural Science Foundation of China [grant number 61573004]; Promotion Program for Young and Middle-aged Teacher in Science and Technology Research of Huaqiao University [grant number ZQN-YX301]; Natural Science Foundation of Fujian Province [grant number 2015J01260]; Program for New Century Excellent Talents in Fujian Province University.