AN N-BARRIER MAXIMUM PRINCIPLE FOR AUTONOMOUS SYSTEMS OF n SPECIES AND ITS APPLICATION TO PROBLEMS ARISING FROM POPULATION DYNAMICS
Journal
Communications on Pure and Applied Analysis
Journal Volume
18
Journal Issue
1
Pages
33-50
Date Issued
2019
Author(s)
Abstract
The main contribution of the N-barrier maximum principle is that it provides rather generic a priori upper and lower bounds for the linear combination of the components of a vector-valued solution. We show that the N-barrier maximum principle (NBMP, C.-C. Chen and L.-C. Hung (2016)) remains true for $n$ $(n>2)$ species. In addition, a stronger lower bound in NBMP is given by employing an improved tangent line method. As an application of NBMP, we establish a nonexistence result for traveling wave solutions to the four species Lotka-Volterra system.