Abstract
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.