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:
where is a bounded domain in
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 .