Acta Mathematicae Applicatae Sinica

, Volume 6, Issue 1, pp 40–43 | Cite as

On the existence theorem of non-trivial periodic solution of periodic systems of high order

  • Zhao Xiaoqiang 


In this paper, we consider nonlinear and nonautonomous systems with the trivial solution:
$${{dx} \mathord{\left/ {\vphantom {{dx} {dt}}} \right. \kern-\nulldelimiterspace} {dt}} = f(t,{\mathbf{ }}x),{\mathbf{ }}x \in R^n $$
wheref(t+ω, x)=f(t, x),f(t, 0)=0. By using the theory of Brouwer topological degree, we obtain the existence theorem of nontrivialω-periodic solution. Finally the applied example of the theorem is cited.


Periodic Solution Existence Theorem Trivial Solution Periodic System Math Application 
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    Zhang Di, On the Existence and Uniqueness of Periodic Solution of Differential Equations of High Order,J. of Northwest University,141(1984), 94–105.Google Scholar
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    Wang Lian, Wang Mu-Qiu, The Stable Oscillation Theorem of the Periodic Dissipative systems of High Order,Scientia Sinica, (A),7(1982), 607–614.Google Scholar
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    Grasman W., Periodic Solution of Autonomous Differential Equations in High Dimensional Spaces,Rocky Mountain J. Math.,73 (1977), 457–466.Google Scholar

Copyright information

© Science Press, Beijing, China and Allerton Press, Inc., New York, U.S.A. 1990

Authors and Affiliations

  • Zhao Xiaoqiang 
    • 1
  1. 1.Institute of Applied MathematicsAcademia SinicaChina

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