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)

Abstract

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.

Keywords

Variational Equation Differential Delay Equation Multiplicative Factor Central Projection Delay Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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