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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,… Click to show full abstract
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.
Journal Title: Journal of Dynamics and Differential Equations
Year Published: 2019
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