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

On the existence theorem of non-trivial periodic solution of periodic systems of high order 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

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

, Volume 6 (1) – Jul 15, 2005
4 pages      /lp/springer-journals/on-the-existence-theorem-of-non-trivial-periodic-solution-of-periodic-ofFhtNKTCD
Publisher
Springer Journals
Copyright © 1990 by Science Press, Beijing, China and Allerton Press, Inc., New York, U.S.A.
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF02014714
Publisher site
See Article on Publisher Site

### 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.

### Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jul 15, 2005

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