General Perturbation of the Exponential Dichotomy for Evolution Equations

Resumo

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 skew-product semiflow technique and a perturbation principle from linear operator Theory. Finally, we apply these results a partial parabolic equation.