Nonexpansive periodic operators in l1 with application to superhigh-frequency oscillations in a discontinuous dynamical system with time delay

Roger D. Nussbaum, Eugenii Shustin

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We prove that the iterates of certain periodic nonexpansive operators in t1 uniformly converge to zero in l norm. As a by-product we show that, for any solution x(t) of the equation x(t)= - sign(*(t - 1))+f(x(t)), t≥0, x| [-1,0] ∈ C[-l,0] where f: ℝ→(-1, 1) is locally Lipschitz, the number of zeros of x(t) on any unit interval becomes finite after a period of time, with the single exception of the case f(0) = 0 and x(t) ≡ 0.

Original languageEnglish (US)
Pages (from-to)381-424
Number of pages44
JournalJournal of Dynamics and Differential Equations
Volume13
Issue number2
DOIs
StatePublished - 2001

All Science Journal Classification (ASJC) codes

  • Analysis

Keywords

  • Differential delay equations
  • Nonexpansive operators

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