A GENERALIZATION OF A PROPOSITION ON EXPONENTIAL DICHOTOMY

It is well known that if x' = A(t)x admits an exponential dichotomy and f(t, x) is a bounded function and has a small Lipschitz constant, then system X' = A(x)x f(t, x) has a unique bounded solution. In this paper, we shall generalize this theorem to the case when f(t, x) is an unbounded function.