It is often conjectured that the existence and uniqueness of solutions to t
he quasi-static Signorini problem with Coulomb friction should hold, provid
ed that the friction coefficient is lower than a critical value. Recently,
the existence of solutions to the quasi-static Signorini problem with non-l
ocal Coulomb friction was shown (M. Cocu, E. Pratt, M. Raous, Int. J. Engng
. Sci. 34 (1996) 783-798) in functional spaces of type W-1.p(0, T) and for
a sufficiently low friction coefficient. In this paper, it is proved that u
niqueness does not hold, in general, for an arbitrarily small friction coef
ficient. (C) 1998 Elsevier Science Ltd. All rights reserved.