This book is devoted to the qualitative theory of functional dynamic equations on time scales, providing an overview of recent developments in the field as well as a foundation to time scales, dynamic systems, and functional dynamic equations. It discusses functional dynamic equations in relation to mathematical physics applications and problems, providing useful tools for investigation for oscillations and nonoscillations of the solutions of functional dynamic equations on time scales. Practice problems are presented throughout the book for use as a graduate-level textbook and as a reference book for specialists of several disciplines, such as mathematics, physics, engineering, and biology.

This books offers the reader an overview of recent developments of functional dynamic equations on time scales, taking readers beyond the traditional calculus texts. The book introduces functional dynamic equations in relation to mathematical physics applications and problems. Useful tools are provided for investigation for oscillations and nonoscillations of the solutions of functional dynamic equations on time scales. This book is suitable for graduate courses and researchers looking for an introduction to functional dynamic equations on time scales.

Autorentext

Martin Bohner - University of Missouri-Rolla, Department of Mathematics and Statistics, Rolla, Missouri. Svetlin G. Georgiev - Sofia University, Faculty of Mathematics and Informatics, Department of Differential Equations, Bulgaria.

Inhalt
Chapter 1- Calculus on Time Scales.- Chapter 2- Dynamic Systems.- Chapter 3- Functional Dynamic Equations. Basic Concepts, Existence and Uniqueness Theorems.- Chapter 4- Linear Functional Dynamic Equations.- Chapter 5- Stability for First Order Functional Dynamic Equations.- Chapter 6- Oscillations of First Order Functional Dynamic Equations.- Chapter 7- Oscillations of Second Order Linear Functional Dynamic Equations with a Single Delay.- Chapter 8- Nonoscillations of Second Order Functional Dynamic Equations with Several Delays.- Chapter 9- Oscillations of Second Order Nonlinear Functional Dynamic Equations.- Chapter 10- Oscillations of Third Order Functional Dynamic Equations.- Chapter 11- Oscillations of Fourth Order Functional Dynamic Equations.- Chapter 12- Oscillations of Higher Order Functional Dynamic Equations.- Chapter 13- Shift Operators.- Chapter 14- Impulsive Functional Dynamic Equations.- Chapter 15- Linear Impulsive Dynamic Systems.- Appendix: Fréchet Derivatives and Gâteaux.- Appendix: Pötzsche's Chain Rule.- Appendix: The Knaster-Tarski Fixed Point Theorem.- Appendix: Some Elementary Inequalities.- Knesser's Theorem.- References.- Index