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An existence result for a functional differential equation on a Banach space

✍ Scribed by Mustapha Yebdri; Fadela Nigro

Publisher: Elsevier Science
Year: 2009
Tongue: English
Weight: 369 KB
Volume: 22
Category: Article
ISSN: 0893-9659
DOI: 10.1016/j.aml.2008.04.008

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✦ Synopsis

We use the nonlinear alternative and topological transversality to prove an existence theorem for the solutions of the functional differential equation ẋ(t) = F (t, x t ), where x t (θ ) = x(t + θ ) for all θ ∈ [-r, 0] and F : [0, A] × X 2 → X , X is a Banach space and X 2 is the Banach space of continuous functions defined on [-r, 0] with values in X .

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