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IMA Journal of Applied Mathematics Advance Access published online on February 24, 2009
IMA Journal of Applied Mathematics, doi:10.1093/imamat/hxp008
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© The Author 2009. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Travelling wave solutions in diffusive and competition–cooperation systems with delays

Kun Li{dagger} and Xiong Li{ddagger}

School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, People's Republic of China

{dagger} Corresponding author. Email: kli{at}mail.bnu.edu.cn

{ddagger} Email: xli{at}bnu.edu.cn

Received on July 9, 2008; Revision received July 9, 2008. Accepted on January 18, 2009

In this paper, travelling wave solutions are considered for two species diffusive and competition–cooperation systems with delays. The method is Schauder's fixed-point theorem and a new cross-iteration scheme for delayed reaction–diffusion systems with partial monotonicity.

Keywords: reaction–diffusion systems; travelling wave solutions; upper and lower solutions; partially quasi-monotonicity.


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