Young Differential Delay Equations Driven by Hölder Continuous Paths

  • Luu Hoang DucEmail author
  • Phan Thanh Hong
Part of the Understanding Complex Systems book series (UCS)


In this paper we prove the existence and uniqueness of the solution of Young differential delay equations under weaker conditions than it is known in the literature. We also prove the continuity and differentiability of the solution with respect to the initial function and give an estimate for the growth of the solution. The proofs use techniques of stopping times, Shauder-Tychonoff fixed point theorem and a Gronwall-type lemma.



We would like to thank the anonymous referees for their careful reading and insightful remarks which led to improvement of our manuscript. This research is partly funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) and by Thang Long University.


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© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Max Planck Institute for Mathematics in the SciencesLeipzigGermany
  2. 2.Institute of MathematicsVietnam Academy of Science and TechnologyHanoiVietnam
  3. 3.Thang Long UniversityHanoiVietnam

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