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Volume 7, Number 2, 2017, Pages 523-531                                                                DOI:10.11948/2017032
On the reflecting function and the qualitative behavior of solutions of some non-autonomous differential equations
Zhengxin Zhou
Keywords:Reflecting function, periodic solution, center conditions, non-autonomous equations.
Abstract:
      In this article, we use the Mironenko's method to discuss the qualitative behavior of some non-autonomous differential equations. We study the structure of the reflecting functions of the simplest differential equations, and obtain some sufficient conditions under which these equations have the rational reflecting functions. We apply the obtained results to discuss the numbers of periodic solutions of the non-autonomous differential systems and derive some sufficient conditions for a critical point of theirs to be a center.
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