Smoothness of Center Manifolds for Maps and Formal Adjoints for Semilinear FDEs in General Banach Spaces

Abstract

We develop a formal adjoint theory for retarded linear functional differential equations in Banach spaces and establish the existence and smoothness of center manifolds for nonlinearly perturbed equations. The hypotheses imposed here are significantly weaker than those that usually appear in the literature referring to semigroups for abstract functional differential equations, and the smoothness of the center manifolds for nonlinear perturbed equations is derived from our general results on the smoothness of center manifolds for maps in infinite-dimensional Banach spaces.