Functional Dynamic Equations on Time Scales

"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." -- Prové de l'editor Front Matter ....Pages i-x Calculus on Time Scales (Svetlin G. Georgiev)....Pages 1-36 Dynamic Systems (Svetlin G. Georgiev)....Pages 37-98 Functional Dynamic Equations. Basic Concepts, Existence, and Uniqueness Theorems (Svetlin G. Georgiev)....Pages 99-139 Linear Functional Dynamic Equations (Svetlin G. Georgiev)....Pages 141-159 Stability for First-Order Functional Dynamic Equations (Svetlin G. Georgiev)....Pages 161-254 Oscillations of First-Order Functional Dynamic Equations (Svetlin G. Georgiev)....Pages 255-345 Oscillations of Second-Order Linear Functional Dynamic Equations with a Single Delay (Svetlin G. Georgiev)....Pages 347-374 Nonoscillations of Second-Order Functional Dynamic Equations with Several Delays (Svetlin G. Georgiev)....Pages 375-406 Oscillations of Second-Order Nonlinear Functional Dynamic Equations (Svetlin G. Georgiev)....Pages 407-468 Oscillations of Third-Order Functional Dynamic Equations (Svetlin G. Georgiev)....Pages 469-547 Oscillations of Fourth-Order Functional Dynamic Equations (Svetlin G. Georgiev)....Pages 549-664 Oscillations of Higher-Order Functional Dynamic Equations (Svetlin G. Georgiev)....Pages 665-748 Shift Operators (Svetlin G. Georgiev)....Pages 749-780 Impulsive Functional Dynamic Equations (Svetlin G. Georgiev)....Pages 781-817 Linear Impulsive Dynamic Systems (Svetlin G. Georgiev)....Pages 819-835 Back Matter ....Pages 837-885