Topics in Almost Automorphy (eBook)

Gaston M. N'Guérékata (Autor)

eBook Download: PDF

2007 | 2005
XII, 168 Seiten
Springer US (Verlag)
978-0-387-27439-3 (ISBN)

Infos

Since the publication of our first book [80], there has been a real resiu-gence of interest in the study of almost automorphic functions and their applications ([16, 17, 28, 29, 30, 31, 32, 40, 41, 42, 46, 51, 58, 74, 75, 77, 78, 79]). New methods (method of invariant s- spaces, uniform spectrum), and new concepts (almost periodicity and almost automorphy in fuzzy settings) have been introduced in the literature. The range of applications include at present linear and nonlinear evolution equations, integro-differential and functional-differential equations, dynamical systems, etc...It has become imperative to take a bearing of the main steps of the the­ ory. That is the main purpose of this monograph. It is intended to inform the reader and pave the road to more research in the field. It is not a self contained book. In fact, [80] remains the basic reference and fimdamental source of information on these topics. Chapter 1 is an introductory one. However, it contains also some recent contributions to the theory of almost automorphic functions in abstract spaces. VIII Preface Chapter 2 is devoted to the existence of almost automorphic solutions to some Unear and nonUnear evolution equations. It con­ tains many new results. Chapter 3 introduces to almost periodicity in fuzzy settings with applications to differential equations in fuzzy settings. It is based on a work by B. Bede and S. G. Gal [40].

Inhalt

Preface 6
Contents 9
Introduction and Preliminaries 11
1.1 Measurable Functions 11
1.2 Sobolev Spaces 15
1.3 Semigroups of Linear Operators 17
1.4 Fractional Powers of Operators 18
1.5 Evolution Equations 19
1.6 Almost Automorphic Functions 22
1.7 Almost Periodic Functions 44
1.8 Bibliographical Remarks and Open Problems 49
Almost Automorphic Evolution Equations 51
2.1 Linear Equations 51
2.2 Nonlinear Equations 66
2.3 Optimal weak- almost periodic solutions 83
2.4 Existence of Weakly Almost Automorphic Solutions 92
2.5 A Correspondence Between Linear and Nonlinear Equations 98
Bibliographical Remarks and Open Problems 103
Almost Periodicity in Fuzzy Setting 105
3.1 Fuzzy Sets 105
3.2 Almost Periodicity in Fuzzy Setting 108
3.3 Harmonics of Almost Periodic Functions in Fuzzy Setting 115
3.4 Applications to Fuzzy Differential Equations 126
3.5 Bibliographical Remarks and Open Problems 131
Almost Automorphy in Fuzzy Setting 132
4.1 Introduction 132
4.2 Preliminaries 133
4.3 Basic Definitions and Properties 139
4.4 Applications to Fuzzy Differential Equations 161
4.5 Bibliographical Remarks and Open Problems 166
References 167
Index 175

Produkt-Details

• Erscheint lt. Verlag: 10.7.2007
• Zusatzinfo: XII, 168 p.
• Verlagsort: New York
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Informatik ► Theorie / Studium
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Naturwissenschaften
• Themenwelt: Technik
• Schlagworte: differential equation • Dynamical Systems • hyperbolic equation • Mathematica • Partial differential equations • Sobolev Space
• ISBN-10: 0-387-27439-1 / 0387274391
• ISBN-13: 978-0-387-27439-3 / 9780387274393