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)


Let M be a separable C finite dimensional connected manifold, I the closed interval [−r, 0], r > 0, and C0(I, M) the totality of continuous maps ϕ of I into M. Let TM be the tangent bundle of M and τM: TM → M its C-canonical projection. Assume there is given on M a complete Riemannian structure (it exists because M is separable) with δM the associated complete metric. This metric on M induces an admissible metric on C0(I, M) by
$$\delta (\varphi ,\bar \varphi ) = \sup \{ {\delta _M}(\varphi (\theta ),\bar \varphi (\theta )):\theta \in I\} .$$


Banach Space Tangent Bundle Functional Differential Equation Tubular Neighborhood Continuous Semigroup 
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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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