This paper is a nice contribution to the study of asymptotic behavior of solutions of semilinear evolution equations. Using the characterization of the exponential dichotomy of evolution equations, the existence of invariant manifolds for the evolution equation is obtained under more general conditions on the nonlinear term
. And, the assumption of uniform Lipschitz continuity of the nonlinear term
is actually replaced by its non-uniform Lipschitz continuity. Generally speaking, this is a good article being worth reading.