Chapter 4

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


We shall introduce, in this chapter, several possible areas of investigation of dynamic systems on time scales that await further progress. In Section 4.1, we shall develop the methods of upper and lower solutions and monotone iterative technique for initial and periodic boundary value problems. Section 4.2 is devoted to the method of generalized quasilinearization which offers not only monotone sequences that converge to the unique solution but also shows that the convergence is quadratic.


Riccati Equation Invariant Manifold Invariance Principle Nonoscillatory Solution Monotone Sequence 
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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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