Positive steady states for a prey-predator cross-diffusion system with a protection zone and Holling type II functional response

Kazuhiro Oeda

doi:10.3934/proc.2013.2013.597

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2013, Volume 2013: 597-603. Doi: 10.3934/proc.2013.2013.597 open access

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Positive steady states for a prey-predator cross-diffusion system with a protection zone and Holling type II functional response

Kazuhiro Oeda^1,

1.
Department of Applied Mathematics, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555

Received: August 31, 2012

Revised: February 28, 2013

Published: October 2013

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Abstract

This paper is concerned with the steady state problem of a prey-predator cross-diffusion system with a protection zone and Holling type II functional response. A sufficient condition for the existence of positive steady state solutions is given. Our proof is based on the bifurcation theory and some a priori estimates.

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Mathematics Subject Classification: Primary: 35B32, 35J57; Secondary: 92D25.

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