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TitleAdvances in Dynamic Equations on Time Scales [electronic resource] / edited by Martin Bohner, Allan Peterson
ImprintBoston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 2003
Connect tohttp://dx.doi.org/10.1007/978-0-8176-8230-9
Descript XI, 348 p. online resource

SUMMARY

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

1. Introduction to the Time Scales Calculus -- 2. Some Dynamic Equations -- 3. Nabla Dynamic Equations -- 4. Second Order Self-Adjoint Equations with Mixed Derivatives -- 5. Riemann and Lebesgue Integration -- 6. Lower and Upper Solutions of Boundary Value Problems -- 7. Positive Solutions of Boundary Value Problems -- 8. Disconjugacy and Higher Order Dynamic Equations -- 9. Boundary Value Problems on Infinite Intervals -- 10. Symplectic Dynamic Systems


Mathematics Differential equations Applied mathematics Engineering mathematics System theory Computer mathematics Mathematics Computational Mathematics and Numerical Analysis Ordinary Differential Equations Applications of Mathematics Systems Theory Control



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