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1996 Positive steady states for prey-predator models with cross-diffusion
Kimie Nakashima, Yoshio Yamada
Adv. Differential Equations 1(6): 1099-1122 (1996).

Abstract

This paper is concerned with the existence of positive solutions for boundary value problems of nonlinear elliptic systems which arise in the study of the Lotka-Volterra prey-predator model with cross-diffusion. Making use of the theory of the fixed point index we can derive sufficient conditions for the coexistence of positive steady states. Moreover, when cross-diffusion effects are comparatively small, we can get a necessary and sufficient condition for the coexistence. The uniqueness result is also given in the special case when the spatial dimension is one.

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Kimie Nakashima. Yoshio Yamada. "Positive steady states for prey-predator models with cross-diffusion." Adv. Differential Equations 1 (6) 1099 - 1122, 1996.

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Published: 1996
First available in Project Euclid: 25 April 2013

zbMATH: 0863.35034
MathSciNet: MR1409901

Subjects:
Primary: 35Q80
Secondary: 35B05 , 35K57 , 92D25 , 92D40

Rights: Copyright © 1996 Khayyam Publishing, Inc.

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Vol.1 • No. 6 • 1996
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