Examples of Retarded Functional Differential Equations on Manifolds

  • Jack K. Hale
  • Luis T. Magalhães
  • Waldyr M. Oliva
Part of the Applied Mathematical Sciences book series (AMS, volume 47)


Autonomous retarded functional differential equations on ℝn are usually defined as equations of the form
$$\dot x\left( t \right) = f\left( {{x_t}} \right)$$
where f maps C0(I, ℝn) into ℝn. Taking M = ℝn and identifying TM with ℝn × ℝn, one can define the function F: C0(I,M) → TM such that F(φ) = φ (0), f(φ)). If f is continuous, then F is an RFDE on M = ℝn which can be identified with the above equation.


Variational Equation Differential Delay Equation Multiplicative Factor Central Projection Delay Equation 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • Jack K. Hale
    • 1
  • Luis T. Magalhães
    • 2
  • Waldyr M. Oliva
    • 3
  1. 1.Division of Applied MathematicsBrown UniversityProvidenceUSA
  2. 2.Universidade Tecnica de LisbõaLisbonPortugal
  3. 3.Departmento de Matemática Aplicada, Instituto de Matemática e EstatisticaUniversidade de São PauloSão PauloBrasil

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