Computational fixed-point theory for differential delay equations with multiple time lags

Gábor Kiss*, Jean Philippe Lessard

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

24 Citations (Scopus)


We introduce a general computational fixed-point method to prove existence of periodic solutions of differential delay equations with multiple time lags. The idea of such a method is to compute numerical approximations of periodic solutions using Newton's method applied on a finite dimensional projection, to derive a set of analytic estimates to bound the truncation error term and finally to use this explicit information to verify computationally the hypotheses of a contraction mapping theorem in a given Banach space. The fixed point so obtained gives us the desired periodic solution. We provide two applications. The first one is a proof of coexistence of three periodic solutions for a given delay equation with two time lags, and the second one provides rigorous computations of several nontrivial periodic solutions for a delay equation with three time lags.

Original languageEnglish
Pages (from-to)3093-3115
Number of pages23
JournalJournal of Differential Equations
Issue number4
Publication statusPublished - 15 Feb 2012
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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