The existence and structure of large spiky steady states forS-K-T competition systems with cross-diffusion

Abstract

This paper is concerned with the existence of large positive spikysteady states for S-K-T competition systems with cross-diffusion.Firstly by detailed integral and perturbation estimates, theexistence and detailed fast-slow structure of a class of spikysteady states are obtained for the corresponding shadow system,which also verify and extend some existence results on spiky steadystates obtained in [10] by different method of proof. Furtherby applying special perturbation method, we prove the existence oflarge positive spiky steady states for the original competitionsystems with large cross-diffusion rate.