Advances in Dynamic Equations on Time Scales

ISBN-13: 9781461265023 / Angielski / Miękka / 2012 / 348 str.

Martin Bohner; Allan C. Peterson; Allan C. Peterson

Opis

Excellent introductory material on the calculus of time scales and dynamic equations.; Numerous examples and exercises illustrate the diverse application of dynamic equations on time scales.; Unified and systematic exposition of the topics allows good transitions from chapter to chapter.; Contributors include Anderson, M. Bohner, Davis, Dosly, Eloe, Erbe, Guseinov, Henderson, Hilger, Hilscher, Kaymakcalan, Lakshmikantham, Mathsen, and A. Peterson, founders and leaders of this field of study.; Useful as a comprehensive resource of time scales and dynamic equations for pure and applied mathematicians.; Comprehensive bibliography and index complete this text.

Recenzje

From the reviews:

"The book can be used as a textbook for a second course in dynamic equations...and is an indispensable mongraph for every researcher in the field of dynamic equations on time scale and related topics." ---Mathmatica Bohemica

"The monograph under review comes at an excellent time in the rapid development of dynamic equations on time scales. Both authors are authorities in this field of study and they have produced an excellent introduction to it. Much of the material is accessible to upper-level undergraduate mathematics majors, and yet, the results and the techniques are pertinent to active researchers in the area."(MATHEMATICAL REVIEWS)

Spis treści

Introduction to the The Time Scales Calculus (Bohner/Guseinov/Peterson) * Some Dynamic Equations (Akin-Bohner/Bohner) * Nabla Dynamic Equations (Anderson/Bullock/Erbe/Peterson/Tran) * Second-Order Self-Adjoint Equations with Mixed Derivatives (Messer) * Riemann and Lebesgue Integration (Bohner/Guseinov) * Lower and Upper Solutions for Two Point Boundary Value Problems (Akin-Bohner/Atici/Kaymakçalan) * Positive Solutions of Boundary Value Problems (Anderson/Avery/Davis/Henderson/Yin) * Disconjugacy and Higher Order Dynamic Equations (Eloe) * Boundary Value Problems on Infinite Intervals: A Topological Approach (Agarwal/Bohner/O'Regan) * Symplectic Dynamic Systems (Dosly/Hilger/Hilscher) * Bibliography * Index

O autorze

The subject of dynamic equations on time scales continues to be a rapidly growing area of research. Behind the main motivation for the subject lies the key concept that dynamic equations on time scales is a way of unifying and extending continuous and discrete analysis. This work goes beyond an earlier introductory text "Dynamic Equations on Time Scales: An Introduction with Applications" (ISBN 0-8176-4225-0) and is designed for a second course in dynamic equations at the graduate level. It will also be valuable to pure and applied mathematicians in the field.

Blurb

The subject of dynamic equations on time scales continues to be a rapidly growing area of research. Behind the main motivation for the subject lies the key concept that dynamic equations on time scales is a way of unifying and extending continuous and discrete analysis.
This work goes beyond an earlier introductory text Dynamic Equations on Time Scales: An Introduction with Applications (ISBN 0-8176-4225-0) and is designed for a second course in dynamic equations at the graduate level.
Key features of the book:
excellent introductory material on the calculus of time scales and dynamic equations * numerous examples and exercises * covers the following topics: the exponential function on time scales, boundary value problems, positive solutions, upper and lower solutions of dynamic equations, integration theory on time scales, disconjugacy and higher order dynamic equations, delta, nabla, and alpha dynamic equations on time scales * unified and systematic exposition of the above topics with good transitions from chapter to chapter * useful for a second course in dynamic equations at the graduate level, with directions suggested for future research * comprehensive  bibliography and index * useful as a comprehensive resource for pure and applied mathematicians

Contributors: R. Agarwal, E. Akin-Bohner, D. Anderson, F. Merdivenci Atici, R. Avery, M. Bohner, J. Bullock, J. Davis, O. Dosly, P. Eloe, L. Erbe, G. Guseinov, J. Henderson, S. Hilger, R. Hilscher, B. Kaymakalan, K. Messer, D. O'Regan, A. Peterson, H. Tran, W. Yin