Continuous selections of set of mild solutions of evolution inclusions
Date
2005-02-11
Authors
Anguraj, Annamalai
Murugesan, Chinnagounder
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
Abstract
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.
Description
Keywords
Mild solutions, Differential inclusions, Integrodifferential inclusions
Citation
Anguraj, A., & Murugesan, C. (2005). Continuous selections of set of mild solutions of evolution inclusions. <i>Electronic Journal of Differential Equations, 2005</i>(21), pp. 1-7.
Rights
Attribution 4.0 International