Topics On Stability And Periodicity In Abstract Differential Equations

by Liu, James H.; N'Guerekata, Gaston M.; Van Minh, Nguyen

• ISBN13: 9789812818232
• ISBN10: 9812818235
• Format: Hardcover
• Copyright: 2008-06-09
• Publisher: World Scientific Pub Co Inc

Summary

"This book presents recent methods of study on the asymptotic behavior of solutions of abstract differential equations such as stability, exponential dichotomy, periodicity, almost periodicity, and almost automorphy of solutions. The chosen methods are described in a way that is suitable to those who have some experience with ordinary differential equations. The book is intended for graduate students and researchers in the related areas."--BOOK JACKET.

Table of Contents

Preliminaries	p. 1
Banach Spaces and Linear Operators	p. 1
Strongly Continuous Semigroups of Operators	p. 7
Spectral Theory	p. 19
Stability and Exponential Dichotomy	p. 39
Perron Theorem	p. 39
Evolution Semigroups and Perron Theorem	p. 47
Stability Theory	p. 51
Comments and Further Reading Guide	p. 58
Almost Periodic Solutions	p. 61
Evolution Semigroups & Periodic Equations	p. 61
Sums of Commuting operators	p. 81
Decomposition Theorem	p. 103
Comments and Further Reading Guide	p. 118
Almost Automorphic Solutions	p. 121
The Inhomogeneous Linear Equation	p. 121
Method of Invariant Subspaces and Almost Automorphic Solutions of Second-Order Differential Equations	p. 127
Existence of Almost Automorphic Solutions to Semilinear Differential Equations	p. 131
Method of Sums of Commuting Operators and Almost Automorphic Functions	p. 135
Almost Automorphic Solutions of Second Order Evolution Equations	p. 139
The Equations x'=f(t,x)	p. 146
Comments and Further Reading Guide	p. 151
Nonlinear equations	p. 153
Periodic Solutions of Nonlinear equations	p. 153
Evolution Semigroups and Almost Periodic Solutions	p. 183
Comments and Further Reading Guide	p. 190
Lipschitz Operators	p. 193
Fixed Point Theorems	p. 195
Invariant Subspaces	p. 197
Semilinear Evolution Equations	p. 198
Bibliography	p. 201
Index	p. 207
Table of Contents provided by Blackwell. All Rights Reserved.