Periodic solutions of abstract functional differential equations with state‐dependent delay |
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| Authors: | Filipe Andrade Claudio Cuevas Hernán R. Henríquez |
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| Affiliation: | 1. Departmento de Matemática, Universidade Federal de Pernambuco, Brazil;2. Departmento de Matemática, Universidad de Santiago‐USACH, Correo‐2, Santiago, Chile |
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| Abstract: | In this paper, we are concerned with the existence of solutions of systems determined by abstract functional differential equations with infinite and state‐dependent delay. We establish the existence of mild solutions and the existence of periodic solutions. Our results are based on local Lipschitz conditions of the involved functions. We apply our results to study the existence of periodic solutions of a partial differential equation with infinite and state‐dependent delay. Copyright © 2016 John Wiley & Sons, Ltd. |
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| Keywords: | retarded functional differential equations abstract functional differential equations state‐dependent delay mild solutions periodic solutions |
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