LaSalle type stationary oscillation theorems for Affine-Periodic Systems

Hongren Wang; Xue Yang; Yong Li; Xiaoyue Li

doi:10.3934/dcdsb.2017156

Article Contents

2017, Volume 22, Issue 7: 2907-2921. Doi: 10.3934/dcdsb.2017156

This issue Previous Article Asymptotic behaviour of an age and infection age structured model for the propagation of fungal diseases in plants Next Article Exponential stability of solutions for retarded stochastic differential equations without dissipativity

LaSalle type stationary oscillation theorems for Affine-Periodic Systems

1.
College of mathematics, Jilin Normal University, Jilin 136000, China
2.
College of Mathematics, Jilin University, Changchun 130012, China
3.
School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China
4.
Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, Changchun 130024, China
5.
Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

* Corresponding author: Yong Li
* Corresponding author: Yong Li

Received: June 30, 2016

Revised: February 28, 2017

Published: October 2017

The second author is supported by NSFC (grant No. 11201173). The third author is supported by National Basic Research Program of China (grant No. 2013CB834100), NSFC (grant No. 11571065) and NSFC (grant No. 11171132).

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Abstract

The paper concerns the existence of affine-periodic solutions for affine-periodic (functional) differential systems, which is a new type of quasi-periodic solutions if they are bounded. Some more general criteria than LaSalle's one on the existence of periodic solutions are established. Some applications are also given.

Keywords:

LaSalle type stationary oscillation principle,
$Q$-affine $T$-periodic solutions,
asymptotic stability.

Mathematics Subject Classification: Primary:34C27;Secondary:34C25.

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References

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