# Nonlinear Delay Evolution Inclusions on Graphs

Marius Popescu*, Mihai Necula and Ioan Vrabie

We prove a necessary and sufficient condition for a time-dependent closed set to be viable with respect to a delay evolution inclusion governed by a strongly-weakly u.s.c. perturbation of a nonlinear $m$-dissipative operator. This condition is expressed in terms of a natural concept involving tangent sets, generalizing tangent vectors in the sense of Bouligand and Severi.

Mathematics Subject Classification: 34K09 34A60 47H20 34G20

Keywords: Differential delay nonlinear inclusion; locally closed graph; tangent set; tangency condition; multi-valued mapping; viability

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