Center manifolds of infinite dimensions. II: Proofs of the main results
type: Item
instance of: scholarly article
title: Center manifolds of infinite dimensions. II: Proofs of the main results
zbMATH Open document ID: 0731.58068
DOI: 10.1007/BF00945799
author: Bruno Scarpellini
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 1991-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 58J60
zbMATH DE Number: 4209176
zbMATH Keywords: infinite dimensions
zbMATH Keywords: Banach space
zbMATH Keywords: Taylor formulas
zbMATH Keywords: fundamental matrix
zbMATH Keywords: center manifold
reviewed by: Michael Th. Rassias
MaRDI profile type: Publication
cites work: Applications of centre manifold theory
cites work: Geometric theory of semilinear parabolic equations
cites work: Q5594071
cites work: Center manifolds of infinite dimensions. I: Main results and applications
cites work: Q3833289
description: scientific article; zbMATH DE number 4209176