A CLASS OF NONLINEAR DELAY EVOLUTION EQUATIONS WITH NONLOCAL INITIAL CONDITIONS

We establish a sufficient condition for the existence, uniqueness and global uniform asymptotic stability of a C-0-solution for the nonlinear delay differential evolution equation { u'(t) is an element of Au(t) + f(t,ut), t is an element of R+, u(t) = g(u) (t), t is an element of [-tau, 0], where tau > 0, X is a real Banach space, A is the infinitesimal generator of a nonlinear semigroup of contractions, f : R+ x C([-tau,0]; <(D(A)))over bar> -> X is continous and g : C-b([-tau +infinity); <(D(A)))over bar> -> C([-tau,0]; <(D(A)))over bar> is nonexpansive.