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| The paper deals with the generalized Gause-type predator-prey system with cross-diffusion and homogeneous Neumann boundary condition, where the cross-diffusion is included in such a way that the prey runs away from the predator. We first give a priori estimate for the positive steady states. Then the non-existence of the non-constant positive steady states is given by employing the energy integral method. Finally, we investigate the existence of the non-constant positive steady states by using the Leray-Schauder degree theory. |
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