Topics On Stability And Periodicity In Abstract Differential Equations
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Topics on Stability and Periodicity in Abstract Differential Equations
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.
Almost Automorphic Type and Almost Periodic Type Functions in Abstract Spaces
Author: Toka Diagana
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-08-13
This book presents a comprehensive introduction to the concepts of almost periodicity, asymptotic almost periodicity, almost automorphy, asymptotic almost automorphy, pseudo-almost periodicity, and pseudo-almost automorphy as well as their recent generalizations. Some of the results presented are either new or else cannot be easily found in the mathematical literature. Despite the noticeable and rapid progress made on these important topics, the only standard references that currently exist on those new classes of functions and their applications are still scattered research articles. One of the main objectives of this book is to close that gap. The prerequisites for the book is the basic introductory course in real analysis. Depending on the background of the student, the book may be suitable for a beginning graduate and/or advanced undergraduate student. Moreover, it will be of a great interest to researchers in mathematics as well as in engineering, in physics, and related areas. Further, some parts of the book may be used for various graduate and undergraduate courses.
Almost Periodicity and Almost Automorphy
Author: Abdallah Afoukal
language: en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date: 2025-03-03
When we study differential equations in Banach spaces whose coefficients are linear unbounded operators, we feel that we are working in ordinary differential equations; however, the fact that the operator coefficients are unbounded makes things quite different from what is known in the classical case. Examples or applications for such equations are naturally found in the theory of partial differential equations. More specifically, if we give importance to the time variable at the expense of the spatial variables, we obtain an “ordinary differential equation” with respect to the variable which was put in evidence. Thus, for example, the heat or the wave equation gives rise to ordinary differential equations of this kind. Adding boundary conditions can often be translated in terms of considering solutions in some convenient functional Banach space. The theory of semigroups of operators provides an elegant approach to study this kind of systems. Therefore, we can frequently guess or even prove theorems on differential equations in Banach spaces looking at a corresponding pattern in finite dimensional ordinary differential equations.