A maximum principle for diffusive Lotka-Volterra systems of two competing species

Using an elementary approach, we establish a new maximum principle for the diffusive Lotka-Volterra system of two competing species, which involves pointwise estimates of an elliptic equation consisting of the second derivative of one function, the first derivative of another function, and a quadratic nonlinearity. This maximum principle gives a priori estimates for the total mass of the two species. Moreover, applying it to the system of three competing species leads to a nonexistence theorem of traveling wave solutions. (C) 2016 Elsevier Inc. All rights reserved.