Existence of traveling wave fronts of delayed Fisher-type equations with degenerate nonlinearities

In this paper, two different kinds of degenerate n-degree Fisher-type equations with delays are considered. Due to the difference of the reaction terms, the existence of traveling front are proved by different methods. More precisely, when the reaction term satisfies the weak quasimonotonicity condition, for c > 2, the existence result is given by the super-sub solution method and the fixed point theorem. Then for c* < c <= 2, where c* is the minimal speed of degenerate p-degree Fisher-type equations without delays, the existence result is proved by the perturbation method and the implicit function theory. For the other type reaction term, we apply the monotone iteration method and the super-sub solution method to obtain the existence conclusion. (C) 2022 Elsevier Ltd. All rights reserved.

Automated summary

This paper considers two different kinds of degenerate n-degree Fisher-type equations with delays. The existence of traveling front is proved by different methods due to the difference of the reaction terms. Specifically, for one type of reaction term satisfying the weak quasimonotonicity condition, the existence result is obtained using the super-sub solution method and the fixed point theorem, while for the other type of reaction term, the existence conclusion is obtained using the monotone iteration method and the super-sub solution method.