Coinvasion–coexistence travelling wave solutions of an integro-difference competition system

Abstract

This paper is concerned with the travelling wave solutions of an integro-difference competition system, of which the purpose is to model the coinvasion–coexistence process of two competitors with age structure. The existence of non-trivial travelling wave solutions is obtained by constructing generalized upper and lower solutions. The asymptotic and non-existence of travelling wave solutions are proved by combining the theory of asymptotic spreading with the idea of contracting rectangle.

Keywords::

• generalized upper and lower solutions
• contracting rectangle
• asymptotic behaviour
• minimal wave speed

Keywords::

• 45C05
• 45M05
• 92D40

Acknowledgements

The authors thank both anonymous reviewers for their helpful comments and suggestions.

Additional information

Funding

The first author was supported by NSF of Gansu Province of China [grant number 1208RJYA004]; Development Program for Outstanding Young Teachers in Lanzhou University of Technology [grant number 1010ZCX019]. The second author was supported by NSF of China [grant number 11101194].