Abstract :
Let X be a separable Banach space. Consider the problem
x9sf t , x ., t)0
D. x 0. sx0gX,
where the continuous function f : w0, `.=XªX is locally Lipschitz continuous in
x, uniformly in t on bounded intervals, and continuous in t uniformly w.r.t. x. The
product integral formula
n T T
x T . slimnª` Iq f i x0 , 0FT-tmax / is0 n n
for the solution x t. of D. has been shown to converge. We also show that if f t, ..
is Lipschitz continuous on X with constant L, then the mapping x0ªx T. is
Lipschitz continuous with constant e LT for any T)0. This formula has been
recently developed for differential inclusions in Rn by Wolenski, but the infinite
dimensional case is considerably more involved.
