Center manifolds of infinite dimensions. II: Proofs of the main results
This paper is a continuation of part I in ibid., No.1, 1-32 (1991; see the review above) in which the author proves Theorem 1, which was stated in part I. This proof establishes the existence of a smooth center manifold, i.e. of a smooth decoupling function for the abstract evolution system considered in part I. The paper concludes with a very interesting appendix in which the proofs of some auxiliary lemmas are presented, some of which were stated in part I, while the others are related to the present proof of Theorem 1. The author in both part I and part II has succeeded to give a very nice new account of the center manifold theory.
scientific article; zbMATH DE number 4209176