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Slowly oscillating periodic solutions for a nonlinear second order differential equation with state-dependent delay


Authors: Ling Zhang and Shangjiang Guo
Journal: Proc. Amer. Math. Soc. 145 (2017), 4893-4903
MSC (2010): Primary 34K13
DOI: https://doi.org/10.1090/proc/13714
Published electronically: June 22, 2017
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Abstract: In this paper, a second order differential equation with state-dependent delay is investigated. The existence of slowly oscillating periodic solutions is established by using Browder's theorem on the existence of a non-ejective fixed point.


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Additional Information

Ling Zhang
Affiliation: School of Mathematics and Physics, China University of Geosciences, Wuhan, Hubei 430074, People’s Republic of China
Email: zhangchong422@126.com

Shangjiang Guo
Affiliation: College of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, People’s Republic of China
Email: shangjguo@hnu.edu.cn

DOI: https://doi.org/10.1090/proc/13714
Keywords: Slowly oscillating, periodic solutions, state-dependent delay
Received by editor(s): July 9, 2016
Received by editor(s) in revised form: December 18, 2016
Published electronically: June 22, 2017
Additional Notes: The first author was supported in part by the National Natural Science Foundation of People’s Republic of China (Grant No. 11626224) and by the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan)
The second author was supported in part by the National Natural Science Foundation of P.R. China (Grants No. 11671123 and 11271115).
Communicated by: Yingfei Yi
Article copyright: © Copyright 2017 American Mathematical Society