In this paper we will establish nonlinear a priori lower and upper bounds for the solutions to a large class of equations which arise from the study of traveling wave solutions of reaction-diffusion equations, and we will apply our nonlinear bounds to the Lotka-Volterra system of two competing species as examples. The idea used in a series of papers \cite{NBMP-Discrete,JDE-16,CPAA-16,DCDS-B-18,NBMP-n-species,DCDS-A-17} for the establishment of the linear N-barrier maximum principle will also be used in the proof.

中文翻译：

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反应扩散方程行波解的非线性估计

在本文中，我们将为研究反应扩散方程的行波解而产生的一大类方程的解建立非线性先验下界和上界，并将我们的非线性界应用于 Lotka-Volterra 系统以两个竞争物种为例。一系列论文中使用的思想\cite{NBMP-Discrete,JDE-16,CPAA-16,DCDS-B-18,NBMP-n-species,DCDS-A-17}用于建立线性N-barrier证明中也将使用极大值原理。