Additional topics

  • Jack K. Hale
  • Sjoerd M. Verduyn Lunel
Part of the Applied Mathematical Sciences book series (AMS, volume 99)


In the previous chapters, we have touched only the surface of the theory of functional differential equations. In recent years, the subject has been investigated extensively and now there are several topics that can be classified as a field in itself. In this chapter, we give an introduction to some of these areas, describe the main results, and occasionally give indications of proofs. We cover generic theory, equations with negative feedback and Morse decompositions, slowly oscillating periodic solutions, singularly perturbed delay equations, averaging, and abstract phase spaces associated with equations with infinite delay. In the supplementary remarks, we give references for the detailed proofs and indicate other areas of functional differential equations that are currently being investigated.


Periodic Solution Periodic Orbit Equilibrium Point Hopf Bifurcation Unstable Manifold 
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Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • Jack K. Hale
    • 1
  • Sjoerd M. Verduyn Lunel
    • 2
  1. 1.Georgia Institute of TechnologySchool of MathematicsAtlantaUSA
  2. 2.Vrije Universiteit AmsterdamAmsterdamThe Netherlands

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