NONLINEAR RETARDED EVOLUTION EQUATIONS WITH NONLOCAL INITIAL CONDITIONS

In this paper we prove sonic sufficient condition for the existence and global uniform asymptotic stability of C-0-solutions for a class of nonlinear retarded differential evolution equation of the form {u'(t) is an element of Au(t) + f (t, u(t), u(t - tau(1)), ... , u(t - tau(n))), t is an element of R+ u(s) = g (u)(s), s is an element of [-tau, 0] where X is a real Banach space, A is the generator of a nonlinear compact semigroup, f : R+ x [<(D(A))over bar>](n+1) -> X is continuous and g : C-b([-tau + infinity); <(D(A))over bar> -> C[-tau, 0] <(D(A)))over bar> is nonexpansive.