ON THE REFLECTING FUNCTION AND THE QUALITATIVE BEHAVIOR OF SOLUTIONS OF SOME NON-AUTONOMOUS DIFFERENTIAL EQUATIONS

Zhengxin Zhou

doi:10.11948/2017032

2017 Volume 7 Issue 2

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Zhengxin Zhou. ON THE REFLECTING FUNCTION AND THE QUALITATIVE BEHAVIOR OF SOLUTIONS OF SOME NON-AUTONOMOUS DIFFERENTIAL EQUATIONS[J]. Journal of Applied Analysis & Computation, 2017, 7(2): 523-531. doi: 10.11948/2017032

Citation:

Zhengxin Zhou. ON THE REFLECTING FUNCTION AND THE QUALITATIVE BEHAVIOR OF SOLUTIONS OF SOME NON-AUTONOMOUS DIFFERENTIAL EQUATIONS[J]. Journal of Applied Analysis & Computation, 2017, 7(2): 523-531. doi: 10.11948/2017032

ON THE REFLECTING FUNCTION AND THE QUALITATIVE BEHAVIOR OF SOLUTIONS OF SOME NON-AUTONOMOUS DIFFERENTIAL EQUATIONS

Zhengxin Zhou

School of Mathematical Sciences, Yangzhou University, Yangzhou, China

Fund Project:

Abstract

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.
- Reflecting function /
- periodic solution /
- center conditions /
- nonautonomous equations
MSC: 34A12;34A34;34C14

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References

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