Abstract:
This paper addresses near viability of a set-valued map graph G with respect to a quasiautonomous
fully nonlinear differential inclusion of the form y
(t) ∈ Ay(t )+F(t, y(t)). We
introduce a new notion of A-quasi-tangency when A is a nonlinear m-dissipative set-valued
operator.We give necessary and sufficient conditions for G to be near viable with respect to
the previous differential inclusion. We obtain under weak hypotheses a classical relaxation
result stating that each solution of the relaxed differential inclusion can be approximated by
a solution of the differential inclusion at any given precision
