We present a unified treatment of discrete, single-step, time-discretized c
ontact problems with Coulomb friction that include quasistatic and dynamic
problems involving rigid or elastic bodies undergoing small or large displa
cements. A general existence theory for these finite-dimensional problems i
s established under broad assumptions that are easily satisfied by many spe
cial models. The proof is based on a homotopy argument. This result extends
many existence results known to date for discrete contact problems. (C) 19
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