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.
|頁（從 - 到）||1085-1112|
|期刊||Proceedings of the Royal Society of Edinburgh Section A: Mathematics|
|出版狀態||已出版 - 12 10月 2014|