Entire solutions for a delayed nonlocal dispersal system with monostable nonlinearities

Yanling Meng, Zhixian Yu, Cheng Hsiung Hsu

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

The paper is concerned with the existence and qualitative properties of entire solutions for a delayed nonlocal dispersal system with monostable nonlinearities. We first prove the existence of traveling wave fronts and a spatially independent solution of the system. Then we establish the comparison principles and some upper estimates for solutions of the system with quasimonotone nonlinearities. Mixing the traveling wave fronts with different wave speeds and the spatially independent solution, we derive the existence of entire solutions for the quasimonotone system. Moreover, we investigate various properties of the entire solutions. Of particular interest is the relationship between the entire solutions and the traveling wave fronts. Finally, by introducing two auxiliary quasimonotone systems, we improve our results to nonquasimonotone systems.

Original languageEnglish
Pages (from-to)1206-1236
Number of pages31
JournalNonlinearity
Volume32
Issue number4
DOIs
StatePublished - 4 Mar 2019

Keywords

  • entire solution
  • Nonlocal dispersal
  • traveling wave front

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