Coexistence periodic solutions of a doubly nonlinear parabolic system with Neumann boundary conditions

Abstract

a b s t r a c tThis paper is concerned with a competitive and cooperative mathematical model for two biological populations which dislike crowding, diffuse slowly and live in a common territory under different kind of intra-and inter-specific interferences. The model consists of a system of two doubly nonlinear parabolic equations with nonlocal terms and Neumann boundary conditions. Based on the theory of the Leray-Schauder degree, we obtain the coexistence periodic solutions, namely the existence of two non-trivial non-negative periodic solutions representing the densities of the two interacting populations, under different intra-and inter-specific interferences on their natural growth rates.

Periodic Problem for Doubly Nonlinear Evolution Equation

“…Compared with Cauchy problem, there are a few results for the existence of timeperiodic solution to doubly nonlinear equation. Periodic problem for (2) is considered in [2] [29] [32] [33] and concrete PDEs of the same type as (2) in [24] [25] [45] [48] [49] [50]. However, to the best of our knowledge, the investigation into other types of equations different from (2) can be found only in Akagi-Stefanelli [5].…”