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September  2017, 22(7): 2907-2921. doi: 10.3934/dcdsb.2017156

## 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

Received  July 2016 Revised  March 2017 Published  May 2017

Fund Project: 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).

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.

Citation: Hongren Wang, Xue Yang, Yong Li, Xiaoyue Li. LaSalle type stationary oscillation theorems for Affine-Periodic Systems. Discrete & Continuous Dynamical Systems - B, 2017, 22 (7) : 2907-2921. doi: 10.3934/dcdsb.2017156
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