Unbounded Perturbation of the Exponential Dichotomy for Evolution Equations

In this paper we prove that the exponential dichotomy for evolution equations in Banach spaces is not destroyed, if we perturb the equation by “small” unbounded linear operator. This is done by employing a skew-product semiflow technique and a perturbation principle from linear operator theory. Finally, we apply these results to partial parabolic equations and functional differential equations.