On a predator-prey system with cross-diffusion representing the tendency of prey to keep away from its predators. (English) Zbl 1170.35549

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.


35Q92 PDEs in connection with biology, chemistry and other natural sciences
35J55 Systems of elliptic equations, boundary value problems (MSC2000)
92D25 Population dynamics (general)
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