An ill-posed mechanical problem with friction

Many models involve the Coulomb's law in order to describe dynamical proper ties of friction phenomena. In order to generalize this Coulomb's law and t o deal with its correct mathematical expression, we study a nonlinear equat ion where we take into account a maximal monotone graph. In the particular case of Coulomb's law, existence and uniqueness are proved. But in the gene ral case, only existence persists. A counter-example to uniqueness is given . (C) Elsevier, Paris.