期刊
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
卷 34, 期 1, 页码 173-203出版社
SIAM PUBLICATIONS
DOI: 10.1137/S0036141001384971
关键词
functional differential equations in Banach spaces; formal adjoint equations; resolvent compact operators; perturbations; center manifolds; smoothness
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.
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