Existence, uniqueness and attractiveness of a pseudo almost automorphic solutions for some dissipative differential equations in Banach spaces

We give sufficient conditions ensuring the existence, uniqueness and global attractiveness of a pseudo compact almost automorphic solution of the following differential equation: x' (t) = f (t, x(t)) in a Banach space E, where f: R x E -> E is a pseudo almost automorphic function with respect to the first argument. We essentially assume that the function f is dissipative. Then we apply the main results to the following equation: x'(t)+q(t)parallel to x(t)parallel to(alpha)x(t) = f(t) (alpha >= 0). (C) 2009 Elsevier Inc. All rights reserved.