Nonconvex Evolution Inclusions Generated by Time - Dependent Subdifferential Operators
نویسندگان
چکیده
We consider nonlinear nonconvex evolution inclusions driven by time-varying subdifferentials 0(t,x) without assuming that (t,.) is of compact type. We show the existence of extremal solutions and then we prove a strong relaxation theorem. Moreover,r 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.
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