Semilinear delay evolution equations with measures subjected to nonlocal initial conditions

We prove a global existence result for bounded solutions to a class of abstract semilinear delay evolution equations with measures subjected to nonlocal initial data of the form: du(t)={Au(t)+f(t,u t )}dt+dg(t) with t∈R+ and u(t)=h(u)(t) for t∈[−τ,0], with τ≥0. The operator A:D(A)⊆X→X is the infinitesimal generator of a C0 -semigroup, f:R+ ×R([−τ,0];X)→X is continuous, g∈BVloc (R+ ;X) and h:Rb (R + ;X)→R([−τ,0];X) is nonexpansive.