Linearized Stability for Semiflows Generated by a Class of Neutral Equations,with Applications to State-Dependent Delays |
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Authors: | Hans-Otto Walther |
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Institution: | (1) Department of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang, 150001, China; |
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Abstract: | We prove a principle of linearized stability for semiflows generated by neutral functional differential equations of the form x′(t) = g(? x t , x t ). The state space is a closed subset in a manifold of C 2-functions. Applications include equations with state-dependent delay, as for example x′(t) = a x′(t + d(x(t))) + f (x(t + r(x(t)))) with \({a\in\mathbb{R}, d:\mathbb{R}\to(-h,0), f:\mathbb{R}\to\mathbb{R}, r:\mathbb{R}\to-h,0]}\). |
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