Almost Periodic Solutions of Differential Equations in Banach Spaces / Edition 1

by Yoshiyuki Hino, Toshiki Naito, Nguyen VanMinh, Jong Son Shin

Overview

This monograph presents recent developments in spectral conditions for the existence of periodic and almost periodic solutions of inhomogenous equations in Banach Spaces. Many of the results represent significant advances in this area. In particular, the authors systematically present a new approach based on the so-called evolution semigroups with an original decomposition technique. The book also extends classical techniques, such as fixed points and stability methods, to abstract functional differential equations with applications to partial functional differential equations. Almost Periodic Solutions of Differential Equations in Banach Spaces will appeal to anyone working in mathematical analysis.

Product Details

ISBN-13:	9780415272667
Publisher:	Taylor & Francis
Publication date:	10/25/2001
Series:	Stability and Control: Theory, Methods and Applications
Pages:	258
Product dimensions:	7.00(w) x 10.00(h) x (d)
Age Range:	18 Years

About the Author

Yoshiyuki Hino, Toshiki Naito, Nguyen VanMinh, Jong Son Shin

Table of Contents

Semigroups. Well-Posed Evolution Equations. Spectral Theory and Almost Periodicity of Functions. Strongly continuous Semigroups of Linear Operators. Evolution Equations. Spectral Theory and Almost Periodicity of Bounded Uniformly Continuous Functions. Spectral Criteria for Periodic and Almost Periodic Solutions. Evolution Semigroups & Almost Periodic Solutions of Periodic Equations. Evolution Semigroups. Sums of Commuting Operators and Spectral Criteria for Almost Periodicity. Decomposition Theorem and Periodic and Almost Periodic Solutions of Periodic Equations. Fixed Point Theorems and Fredholm Operators. Boundedness and Almost Periodicity in Discrete Systems. Boundedness and Almost Periodic Solutions of Semilinear Equations. Notes, Stability Methods for Semilinear Evolution Equations and Nonlinear Evolution Equations. Skew Product Flows of Processes and Quasi-Processes and Stability of Integrals. Existence Theorems of Almost Periodic Integrals. Processes and Quasi-Processes Generated by Abstract Functional Differential Equations. Equivalent Relationships Between BC-Stabilities and P-Stabilities. Existence of Almost Periodic Solutions.

Editorial Reviews

"[U]seful for graduate students and researchers in differential equations, dynamical systems, stability theory, and control theory."
- Zentralblatt fur Mathematik, Vol. 1026

From the Publisher