Advances in Dynamic Equations on Time Scales

1. Front Matter

   Pages i-xi

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2. Introduction to the Time Scales Calculus

   • Martin Bohner, Gusein Guseinov, Allan Peterson

   Pages 1-15

3. Some Dynamic Equations

   • Elvan Akin-Bohner, Martin Bohner

   Pages 17-46

4. Nabla Dynamic Equations

   • Douglas Anderson, John Bullock, Lynn Erbe, Allan Peterson, HoaiNam Tran

   Pages 47-83

5. Second Order Self-Adjoint Equations with Mixed Derivatives

   • Kirsten Messer

   Pages 85-116

6. Riemann and Lebesgue Integration

   • Martin Bohner, Gusein Guseinov

   Pages 117-163

7. Lower and Upper Solutions of Boundary Value Problems

   • Elvan Akin-Bohner, Ferhan Merdivenci Atici, Billûr Kaymakçalan

   Pages 165-188

8. Positive Solutions of Boundary Value Problems

   • Douglas Anderson, Richard Avery, John Davis, Johnny Henderson, William Yin

   Pages 189-249

9. Disconjugacy and Higher Order Dynamic Equations

   • Paul Eloe

   Pages 251-274

10. Boundary Value Problems on Infinite Intervals: A Topological Approach

    • Ravi Agarwal, Martin Bohner, Donal O’Regan

    Pages 275-291

11. Symplectic Dynamic Systems

    • Ondřej Došlý, Stefan Hilger, Roman Hilscher

    Pages 293-334

12. Back Matter

    Pages 335-348

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The development of time scales is still in its infancy, yet as inroads are made, interest is gathering steam. Of a great deal of interest are methods being intro­ duced for dynamic equations on time scales, which now explain some discrepancies that have been encountered when results for differential equations and their dis­ crete counterparts have been independently considered. The explanations of these seeming discrepancies are incidentally producing unifying results via time scales methods. The study of dynamic equations on time scales is a fairly new subject, and research in this area is rapidly growing. It has been created in order to unify continuous and discrete analysis, and it allows a simultaneous treatment of dif­ ferential and difference equations, extending those theories to so-called dynamic equations. An introduction to this subject is given in Dynamic Equations on Time Scales: An Introduction with Applications (MARTIN BOHNER and ALLAN PETER­ SON, Birkhauser, 2001 [86]). The current book is designed to supplement this introduction and to offer access to the vast literature that has already emerged in this field. It consists of ten chapters, written by an international team of 21 experts in their areas, thus providing an overview of the recent advances in the theory on time scales. We want to emphasize here that this book is not just a collection of papers by different authors.

• Boundary value problem
• ODEs
• calculus
• difference equations
• linear optimization
• numerical mathematics
• ordinary differential equations

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)

• Department of Mathematics & Statistics, University of Missouri-Rolla, Rolla, USA

  Martin Bohner

• Department of Mathematics & Statistics, University of Lincoln-Nebraska, Lincoln, USA

  Allan Peterson

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