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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
Content Level »Research
Keywords »Boundary value problem - ODEs - calculus - difference equations - linear optimization - numerical mathematics
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