Method of Constructing Upper-Lower Solutions for Wave Profile Systems with Quasi-Monotonicity

The wave profile systems corresponding to a reaction-diffusion system and an integro-partial differential system with $n (>1)$ equations and quasi-monotonicity are considered. By analyzing the principal eigen-value and eigen-vector, a constructing method of upper-lower solutions for the wave profile systems is given. Some examples to illustrate the applications of our method are given. At last, a brief discussion for the application of this method to the reaction-diffusion system with delay is given.