## Abstract

We are interested in finding the entire solutions of non-quasi-monotone delayed non-local reaction-diffusion equations. It is well known that the comparison principle is not applicable for such equations. To overcome this difficulty, we introduce two auxiliary quasi-monotone equations and establish some comparison arguments for the three systems. Some new types of entire solutions are then constructed using the comparison argument, the travelling wavefronts and a spatially independent solution of the auxiliary equations. We also extend our arguments to a delayed cellular neural network with non-monotonic output functions and a delayed non-local lattice differential equation with non-monotonic birth functions.

Original language | English |
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Pages (from-to) | 1085-1112 |

Number of pages | 28 |

Journal | Proceedings of the Royal Society of Edinburgh Section A: Mathematics |

Volume | 144 |

Issue number | 5 |

DOIs | |

State | Published - 12 Oct 2014 |