Información General

• Autores: Gaston Mandata N'Guérékata
• Editores: New York : Springer, 2005
• Año de publicación: 2005
• País: Estados Unidos
• Idioma: inglés
• ISBN: 978-0-387-22846-4, 978-0-387-27439-3
• Texto completo no disponible (Saber más ...)

Resumen

• This monograph presents recent contributions to the topics of almost periodicity and almost automorphy. Several new methods, including the methods of invariant subspaces and uniform spectrum, as well as various classical methods, such as fixed point theorems, are used to obtain almost periodic and almost automorphic solutions to some linear and non-linear evolution equations and dynamical systems. Almost periodicity and almost automorphy are also intensively developed on the more general structures called fuzzy-number type spaces. They have further potential applications to the study of differential equations, which model the real-world problems governed by imprecision due to uncertainty or vagueness, rather than randomness. In conclusion, the author indicates several open problems and directions for future research. This monograph is a great source of information and inspiration for researchers and graduate students from many mathematical fields.

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Índice

• 1: Introduction and Preliminaries
  1.1 Measurable Functions
  1.2 Sobolev Spaces
  1.3 Semigroups of Linear Operators
  1.4 Fractional Powers of Operators
  1.5 Evolution Equations
  1.6 Almost Automorphic Functions
  1.6.1 Asymptotically Almost Automorphic Functions
  1.6.2 Applications to Abstract Dynamical Systems
  1.7 Almost Periodic Functions
  1.8 Bibliographical Remarks and Open Problems
  2: Almost Automorphic Evolution Equations
  2.1 Linear Equations
  2.1.1 The inhomogeneous equation x’ = Ax + f
  2.1.2 Method of Invariant Subspaces
  2.1.3 Almost Automorphic Solutions to Some Second-Order Hyperbolic Equations
  2.2 Nonlinear Equations
  2.2.1 Existence of Almost Automorphic Mild Solutions-Case I
  2.2.2 Existence of Almost Automorphic Mild Solutions-Case II
  2.3 Optimal weak-almost periodic solutions
  2.4 Existence of Weakly Almost Automorphic Solutions
  2.5 A Correspondence Between Linear and Nonlinear Equations
  3: Almost Periodicity in Fuzzy Setting
  3.1 Fuzzy Sets
  3.2 Almost Periodicity in Fuzzy Setting
  3.3 Harmonics of Almost Periodic Functions in Fuzzy Setting
  3.4 Applications to Fuzzy Differential Equations
  3.5 Bibliographical Remarks and Open Problems
  4: Almost Automorphy in Fuzzy Setting
  4.1 Introduction
  4.2 Preliminaries
  4.3 Basic Definitions and Properties
  4.4 Applications to Fuzzy Differential Equations
  4.5 Bibliographical Remarks and Open Problems
  References
  Index