Approximate invariance and differential inclusions in Hilbert spaces

@inproceedings{HA1999ApproximateIA,
title={Approximate invariance and differential inclusions in Hilbert spaces},
author={F. H.A. and Sergei Yu. and M. Li},
year={1999}
}

Consider a mapping F from a Hilbert space H to the subsets of H which is upper semicontinuous/Lipschitz, has nonconvex, noncompact values and satisfies to a linear growth condition. We give necessary and sufficient conditions for a subset S of H to be approximately weak/strong invariant with respect to approximate solutions of the differential inclusion ẋ(t) ∈ F (x). The conditions are given in terms of the lower/upper Hamiltonians corresponding to F and involve nonsmooth analysis elements and… CONTINUE READING