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Zbl 1170.35549
Ko, Wonlyul; Ryu, Kimun
On a predator-prey system with cross-diffusion representing the tendency of prey to keep away from its predators. (English)
[J] Appl. Math. Lett. 21, No. 11, 1177-1183 (2008). ISSN 0893-9659

Summary: We study a predator-prey system with cross-diffusion, representing the tendency of prey to keep away from its predators, under the homogeneous Dirichlet boundary condition. Using fixed point index theory, we provide some sufficient conditions for the existence of positive steady-state solutions. Furthermore, we investigate the non-existence of positive solutions.
MSC 2000:
*35Q80 Appl. of PDE in areas other than physics
35J55 Systems of elliptic equations, boundary value problems
92D25 Population dynamics

Keywords: predator-prey interaction; cross-diffusion; index theory

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