Uniqueness and symmetry of equilibria in a chemotaxis model

Abstract We consider in a disc of a class of parameter-dependent, nonlocal elliptic boundary value problems that describes the steady states of some chemotaxis systems. If the appearing parameter is less than an explicit critical value, we establish several uniqueness results for solutions that are invariant under a group of rotations. Furthermore, we discuss the associated consequences for the time asymptotic behavior of the solutions to the corresponding time dependent chemotaxis systems. Our results also provide optimal constants in some Moser–Trudinger type inequalities.

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