Advances in Differential Equations
- Adv. Differential Equations
- Volume 1, Number 6 (1996), 1099-1122.
Positive steady states for prey-predator models with cross-diffusion
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.
Adv. Differential Equations Volume 1, Number 6 (1996), 1099-1122.
First available in Project Euclid: 25 April 2013
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Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35Q80: PDEs in connection with classical thermodynamics and heat transfer
Secondary: 35B05: Oscillation, zeros of solutions, mean value theorems, etc. 35K57: Reaction-diffusion equations 92D25: Population dynamics (general) 92D40: Ecology
Nakashima, Kimie; Yamada, Yoshio. Positive steady states for prey-predator models with cross-diffusion. Adv. Differential Equations 1 (1996), no. 6, 1099--1122. https://projecteuclid.org/euclid.ade/1366895246.