Periodic traveling wave solutions of periodic integrodifference systems

Guo Lin; Shuxia Pan

doi:10.3934/dcdsb.2020049

Article Contents

2020, Volume 25, Issue 8: 3005-3031. Doi: 10.3934/dcdsb.2020049

This issue Previous Article Spectral theory and time asymptotics of size-structured two-phase population models Next Article The limits of solutions of a linear delay integral equation

Periodic traveling wave solutions of periodic integrodifference systems

Guo Lin^1, and
Shuxia Pan^2,

1.
School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, China
2.
School of Science, Lanzhou University of Technology, Lanzhou, Gansu 730050, China

Received: March 2019

Revised: September 2019

Early access: February 2020

Published: August 2020

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Abstract

This paper is concerned with the periodic traveling wave solutions of integrodifference systems with periodic parameters. Without the assumptions on monotonicity, the existence of periodic traveling wave solutions is deduced to the existence of generalized upper and lower solutions by fixed point theorem and an operator with multi steps. The asymptotic behavior of periodic traveling wave solutions is investigated by the stability of periodic solutions in the corresponding initial value problem or the corresponding difference systems. To illustrate our conclusions, we study the periodic traveling wave solutions of two models including a scalar equation and a competitive type system, which do not generate monotone semiflows. The existence or nonexistence of periodic traveling wave solutions with all positive wave speeds is presented, which implies the minimal wave speeds of these models.

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Mathematics Subject Classification: Primary: 35K57, 37C65; Secondary: 92D25.

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