Continuous selections of set of mild solutions of evolution inclusions
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We prove the existence of continuous selections of the set valued map ξ → S(ξ) where S(ξ) is the set of all mild solutions of the evolution inclusions of the form
ẋ(t) ∈ A(t)x(t) + ∫t0 K(t, s) F(s, x(s))ds
x(0) = ξ, t ∈ I = [0, T],
where F is a lower semi continuous set valued map Lipchitzean with respect to x in a separate Banach space X, A is the infinitesimal generator of a C0-semi group of bounded linear operators from X to X, and K(t, s) is a continuous real valued function defined on I x I with t ≥ s for all t, s ∈ I and ξ ∈ X.
CitationAnguraj, A., & Murugesan, C. (2005). Continuous selections of set of mild solutions of evolution inclusions. Electronic Journal of Differential Equations, 2005(21), pp. 1-7.
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