Abstract
In this paper, we consider the following system [Formula: see text] which corresponds to the stationary system of a generalized volume-filling chemotaxis model with logistic source in a bounded domain in [Formula: see text] with zero Neumann boundary conditions. Here the parameters [Formula: see text] are positive and [Formula: see text], and [Formula: see text] denotes the outward unit normal vector of [Formula: see text]. With the priori positive lower- and upper-bound solutions derived by the Moser iteration technique and maximum principle, we apply the degree index theory in an annulus to show that if the chemotactic coefficient [Formula: see text] is suitably large, the system with [Formula: see text] admits pattern solutions under certain conditions. Numerical simulations of the pattern formation are shown to illustrate the theoretical results and predict the interesting phenomenon for further studies.
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