Acta Mathematicae Applicatae Sinica

, Volume 6, Issue 1, pp 40–43

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

• Zhao Xiaoqiang
Article

## Abstract

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.

### Keywords

Periodic Solution Existence Theorem Trivial Solution Periodic System Math Application

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### References

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