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Periodic solutions of abstract functional differential equations with state‐dependent delay
Author(s) -
Andrade Filipe,
Cuevas Claudio,
Henríquez Hernán R.
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3837
Subject(s) - mathematics , lipschitz continuity , delay differential equation , state dependent , state (computer science) , differential equation , mathematical analysis , functional differential equation , distributed parameter system , mathematical economics , algorithm
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.