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ISSN 0012-2661, Differential Equations, 2007, Vol. 43, No. 8, pp. 1079–1087. c Pleiades Publishing, Ltd., 2007. Original Russian Text c A.V. Surkov, 2007, published in Differentsial’nye Uravneniya, 2007, Vol. 43, No. 8, pp. 1055–1063. ORDINARY DIFFERENTIAL EQUATIONS On the Stability of Functional-Differential Inclusions with the Use of Invariantly Differentiable Lyapunov Functionals A. V. Surkov Institute for System Dynamics and Control Theory, Siberian Branch, Russian Academy of Sciences, Irkutsk, Russia Received March 16, 2006 DOI: 10.1134/S001226610708006X 1. DEFINITION AND STATEMENT OF THE PROBLEM Let R be the n-dimensional vector space with the Euclidean norm ·,let C be the space of all continuous functions ψ(·) defined on the interval [−τ, 0] and ranging in R with the ordinary sup-norm · =sup ψ(θ), −τ≤θ≤0 1 n and let F : R × C → R be a jointly upper semicontinuous multimapping [1, p. 114 of the Russian translation] with convex compact values. In the present paper, we consider the functional- differential inclusion x ˙ ∈ F (t, x (·)),x (·)= ϕ (·), (1) t t 0 where x (·) ∈ C , x (θ)= x(t + θ), −τ ≤ θ ≤ 0, and ϕ (·) ∈ C is the initial
Differential Equations – Springer Journals
Published: Oct 26, 2007
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