Global stability of almost periodic solutions of monotone sweeping\n processes and their response to non-monotone perturbations

We develop a theory which allows making qualitative conclusions about the\ndynamics of both monotone and non-monotone Moreau sweeping processes.\nSpecifically, we first prove that any sweeping processes with almost periodic\nmonotone right-hand-sides admits a globally exponentially stable almost\nperiodic solution. And then we describe the extent to which such a globally\nstable solution persists under non-monotone perturbations.\n