Nonconvex evolution inclusions generated by time‐dependent subdifferential operators
Kate Arseni-Benou, Nikolaos Halidias, Nikolaos S. Papageorgiou · International Journal of Stochastic Analysis · 1998
We consider nonlinear nonconvex evolution inclusions driven by time‐varying subdifferentials ∂ϕ(t, x) without assuming that ϕ(t.) is of compact type. We show the existence of extremal solutions and then we prove a strong relaxation theorem. Moreover, we show that under a Lipschitz condition on the orientor field, the solution set of the nonconvex problem is path‐connected in C(T, H). These results are applied to nonlinear feedback control systems to derive nonlinear infinite dimensional versions of the “bang‐bang principle.” The abstract results are illustrated by two examples of nonlinear parabolic problems and an example of a differential variational inequality.