Abstract
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 language | English |
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Pages (from-to) | 3093-3115 |
Number of pages | 23 |
Journal | Journal of Differential Equations |
Volume | 252 |
Issue number | 4 |
DOIs | |
Publication status | Published - 15 Feb 2012 |
Externally published | Yes |
ASJC Scopus subject areas
- Analysis
- Applied Mathematics