Perturbation Theory for Dual Semigroups. Part 3. Nonlinear Lipschitz Continuous Perturbations in the Sun-Reflexive Case

摘要

Nonlinear Lipschitz perturbations of the infinitesimal generator of a linear C sub 0-semigroup on a nonreflexive Banach space are considered. It is allowed that the perturbation maps the space into a bigger space which arises in a natural way when considering dual semigroups. Using a generalized variation-of-constants formula, it is shown that the perturbed operator generates a strongly continuous nonlinear semigroup. Regularity properties of this semigroup are studied, and the principle of linearized stability is proved.