Monotonicity and Stability for Some Reaction-Diffusion Systems with Delay and Dirichlet Boundary Conditions

In this work, we are concerned with the monotonicity and the stability study for quasi-monotone reaction-diffusion systems with delay and subject to Dirichlet boundary conditions. We first establish some invariance and comparison results for abstract retarded functional differential equations with nondense domain operators. This allows us to show the monotonicity of the semiflow in a suitable phase space. We also discuss a stability criterion independently of delay