Chapter 1

  • V. Lakshmikantham
  • S. Sivasundaram
  • B. Kaymakcalan
Part of the Mathematics and Its Applications book series (MAIA, volume 370)


In recent times, theory of difference equations has assumed a greater importance as a well deserved discipline because of several reasons. Although there is a striking duality between the theories of differential equations and difference equations, the theory of difference equations is a lot richer than the corresponding theory of differential equations, and often demands additional assumptions to overcome the topological deficiency of lacking connectedness. None the less, it is natural to seek a framework which permits us to handle both dynamic systems simultaneously in order to get better insight and understanding of the subtle differences of the two systems. Recently developed theory of dynamic systems on time scales (closed sets of reals) provides the desired unified approach.


Topological Space Difference Equation Order Topology Jump Operator Induction Principle 
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Copyright information

© Springer Science+Business Media Dordrecht 1996

Authors and Affiliations

  • V. Lakshmikantham
    • 1
  • S. Sivasundaram
    • 2
  • B. Kaymakcalan
    • 3
  1. 1.Division of Interdisciplinary ProgramsFlorida Institute of TechnologyMelbourneUSA
  2. 2.Department of MathematicsEmbry-Riddle Aeronautical UniversityDaytona BeachUSA
  3. 3.Middle East Technical UniversityAnkaraTurkey

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