This paper deals with two-species convolution diffusion-competition models of Lotka–Volterra type with delays which describe more accurate information than the Laplacian diffusion-competition models. We first investigate the existence of travelling wave solutions of a class of nonlocal convolution diffusion systems with weak quasimonotonicity or weak exponential quasimonotonicity by a cross-iteration technique and Schauder’s fixed point theorem. When the results are applied to the convolution diffusion-competition models with delays, we establish the existence of travelling wave solutions as well as asymptotic behaviour.
(Received April 17 2009)
(Revised August 14 2009)
2000 Mathematics subject classificationprimary 35K57; secondary 92D25; 35R10
Keywords and phrasestravelling wave solutions; convolution; cross-iteration; Schauder’s fixed point theorem