Entire solutions of non-quasi-monotone delayed reaction-diffusion equations with applications

Shi Liang Wu, Cheng Hsiung Hsu

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


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 languageEnglish
Pages (from-to)1085-1112
Number of pages28
JournalProceedings of the Royal Society of Edinburgh Section A: Mathematics
Issue number5
StatePublished - 12 Oct 2014


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