ABSTRACT
In this chapter, we prove an existence result for bounded C0-solutions to a class of nonlinear functional differential evolution inclusions subjected to nonlocal initial conditions of the form
u′(t) ∈ Au(t) + f(t), t ∈ R+, f(t) ∈ F (t, ut), t ∈ R+, u(t) = g(u)(t), t ∈ [−τ, 0 ],
(7.1.1)
where X is a Banach space, τ ≥ 0, the operator A : D(A) ⊆ X X is ω-m-dissipative for a certain ω > 0,
X = C([−τ, 0 ];X) and D = {ϕ ∈ X; ϕ(0) ∈ D(A)}, F : R+ × X X is nonempty, convex, weakly compact-valued and almost strongly-weakly u.s.c., and g :Cb(R+;D(A))→ D is nonexpansive.
