Existence of periodic solutions of dynamic equations on time scales by averaging

Ruichao Guo; Yong Li; Jiamin Xing; Xue Yang

doi:10.3934/dcdss.2017050

Article Contents

2017, Volume 10, Issue 5: 959-971. Doi: 10.3934/dcdss.2017050

This issue Previous Article Mathematical modeling about nonlinear delayed hydraulic cylinder system and its analysis on dynamical behaviors Next Article Global Hopf bifurcation of a population model with stage structure and strong Allee effect

Existence of periodic solutions of dynamic equations on time scales by averaging

a.
College of Mathematics, Jilin University, Changchun, 130012, China
b.
School of Mathematics and Statistics and Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, Changchun 130024, China
c.
State Key Laboratory of Automotive Simulation and control, Jilin University, Changchun, 130012, China

Received: November 30, 2016

Revised: December 31, 2016

Published: October 2017

The first author was supposed by NSFC (grant No. 11301541). The second author was supposed by National Basic Research Program of China (grant No. 2013CB834100), NSFC (grant No. 11571065), NSFC (grant No. 11171132). The fourth author was supposed by NSFC (grant No. 11201173)

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Abstract

In this paper, we study the existence of periodic solutions for perturbed dynamic equations on time scales. Our approach is based on the averaging method. Further, we extend some averaging theorem to periodic solutions of dynamic equations on time scales to $k-$th order in $\varepsilon$. More precisely, results of higher order averaging for finding periodic solutions are given via the topological degree theory.

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Mathematics Subject Classification: Primary: 34C25, 34N05; Secondary: 70K65.

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References

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