Semigroup Properties and the Crandall Liggett Approximation for a Class of Differential Equations with State-Dependent Delays |
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Authors: | M LouihiML Hbid O Arino |
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Institution: | a Department of Mathematics, Faculty of Sciences, University Cadi Ayyad, B.P. S15, Marrakech, Moroccob Institut de Recherche pour le Développement (IRD), 32 avenue Henri Varagnat, F-93143, Bondy, France |
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Abstract: | We present an approach for the resolution of a class of differential equations with state-dependent delays by the theory of strongly continuous nonlinear semigroups. We show that this class determines a strongly continuous semigroup in a closed subset of C0, 1. We characterize the infinitesimal generator of this semigroup through its domain. Finally, an approximation of the Crandall-Liggett type for the semigroup is obtained in a dense subset of (C, ‖·‖∞). As far as we know this approach is new in the context of state-dependent delay equations while it is classical in the case of constant delay differential equations. |
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Keywords: | Geodesic connectedness Multiwarped spacetime Topological methods Brouwer's degree Geodesics in Lorentzian manifolds Lorentzian Lagrangian problems |
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