Stationary patterns of a diffusive model with spatiotemporal delay

A diffusive model with spatiotemporal delay subject to Neumann boundary condition is analyzed in this paper. The stability of the positive constant solutions is discussed. By maximum principle and Harnack inequality, a priori estimate of nonconstant positive steady states is given. Then, the nonexistence and existence of nonconstant positive steady states of the reaction-diffusion model are established, which demonstrates that the large diffusion rate can create stationary patterns.