# Nonstandard Quasi-monotonicity: An Application to the Wave Existence in a Neutral KPP–Fisher Equation

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## Abstract

We revisit Wu and Zou non-standard quasi-monotonicity approach for proving existence of monotone wavefronts in monostable reaction–diffusion equations with delays. This allows to solve the problem of existence of monotone wavefronts in a neutral KPP–Fisher equation. In addition, using some new ideas proposed recently by Solar et al., we establish the uniqueness (up to a translation) of these monotone wavefronts.

## Keywords

Monostable equation Quasi-monotonicity Non-standard order Uniqueness KPP–Fisher delayed equation Neutral differential equation## Mathematics Subject Classification

34K12 35K57 92D25## Notes

### Acknowledgements

This work was initiated during a research stay of S.T. at the São Paulo University at Ribeirão Preto, Brasil. It was supported by FAPESP (Brasil) Project 18/06658-1 and partially by FONDECYT (Chile) Project 1190712. The first author was supported by Fapesp (Brasil) Project 2017/13145-8. S.T. acknowledges the very kind hospitality of the DCM-USP and expresses his sincere gratitude to the Professors M. Pierri and E. Hernández for their support and hospitality.

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