Non-existence of stationary pattern of a chemotaxis model with logistic growth

In this paper we study the non-existence of non-constant steady state (i.e., stationary pattern) for a Chemotaxis model with the volume-filling effect and logistic cell growth. We establish the critical value of the chemotactic coefficient between the existence and the non-existence of stationary pattern. The proofs mainly rely on the Maximum Principle, the Implicit Function Theorem and the Finite Covering Theorem. This work is a supplement and perfection of the known reference.