Non-constant positive solutions of a general Gause-type predator-prey system with self- and cross-diffusions

In this paper, we investigate the non-constant stationary solutions of a general Gause-type predator-prey system with self- and cross-diffusions subject to homogeneous Neumann boundary condition. system, are introduced in such way that prey runs away from predator, while predator moves large group preys. Firstly, establish priori estimate for positive solutions. Secondly, study non-existence results Finally, consider existence discuss Turing instability constant solution.