Invariant Manifolds for Abstract Functional Differential Equations and Related Volterra Difference Equations in a Banach Space

• Murakami Satoru

  Okayama University of Science

• Nagabuchi Yutaka

  Okayama University of Science

Abstract

For abstract functional differential equations (FDE) and Volterra difference equations (VDE) in a Banach space, the local existence and smoothness of invariant manifolds, such as stable/unstable manifolds, center-stable/center-unstable manifolds and center manifolds, are established by means of the variation of constants formula in the phase space in [18] and [12]. Also, it is shown that in a neighborhood of the zero solution the behavior of solutions of FDE (resp. VDE) is described, in some sense, by a certain ordinary differential equation (resp. first order difference equation) in a finite dimensional space. As a corollaly, the principle of linearized stability is derived.

Journal

• Funkcialaj Ekvacioj

  Funkcialaj Ekvacioj 50 (1), 133-170, 2007

  Division of Functional Equations, The Mathematical Society of Japan

Keywords

• Abstract functional differential equations
• Volterra difference equations
• Invariant manifolds
• Principle of linearized stability

Details

• CRID: 1390282680090916864
• NII Article ID: 130000140684
• DOI: 10.1619/fesi.50.133
• MRID: 2332082
• ISSN: 05328721
• Web Site: http://www.jstage.jst.go.jp/article/fesi/50/1/50_1_133/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
• Abstract License Flag: Disallowed