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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.


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