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

Abstract

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.