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Large amplitude stationary solutions to a chemotaxis system. (English) Zbl 0676.35030

The existence of nonconstant stationary solutions to the Keller-Segel model [J. Theor. Biol. 26, 399-415 (1970)] is treated. The problem is reduced to the following single equation:

(1)dΔw-w+w p =0onΩ,w/n=0onΩ,

where Ω is a bounded domain in n ·

It is shown that for d sufficiently small no nonconstant solutions to (1) are possible and for d sufficiently close to 0 there exist uniformly bounded nonconstant solutions. The behaviour of the latter is investigated when d0.

35J65Nonlinear boundary value problems for linear elliptic equations
35B35Stability of solutions of PDE
92CxxPhysiological, cellular and medical topics
35B32Bifurcation (PDE)