Journal of Dynamics and Differential Equations

, Volume 31, Issue 4, pp 2275–2292 | Cite as

Spreading Speeds and Traveling Wave Solutions for a Delayed Periodic Equation without Quasimonotonicity



This paper is concerned with the propagation theory of a delayed periodic equation without quasimonotonicity. Because of time delay, it does not generate a monotone semiflow. A threshold is obtained, which is the spreading speed as well as the minimal wave speed. To estimate the spreading speed, some auxiliary equations are given, which also implies the nonexistence of traveling wave solutions. The existence of traveling wave solutions is investigated by Schauder’s fixed point and regularity of analytic semigroup, and is confirmed by showing the existence of generalized upper and lower solutions.


Nonmonotone equation Upper and lower solutions Auxiliary equations 

Mathematics Subject Classification

35K57 37C65 



The author is grateful to the anonymous referee for his/her careful reading and valuable comments.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsLanzhou UniversityLanzhouPeople’s Republic of China

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