Abstract
In this paper we study existence, uniqueness, and stability of nonlinear evolution equations. We develop a new type of perturbation result for a C 0 semigroup in Banach space, where the nonlinear operators are not necessarily m-accretive or everywhere defined. Assuming that the semigroup has a smoothing property we obtain local existence, uniqueness and regularity results. We then establish a Liapunov theory which enables us to examine stability. To illustrate our theory several simple examples are presented.
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