Asymptotic behavior and oscillation of functional differential equations

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Abstract

Asymptotic relations between the solutions of a linear autonomous functional differential equation and the solutions of the corresponding perturbed equation are established. In the scalar case, it is shown that the existence of a nonoscillatory solution of the perturbed equation often implies the existence of a real eigenvalue of the limiting equation. The proofs are based on a recent Perron type theorem for functional differential equations.

Original languageEnglish
Pages (from-to)1140-1158
Number of pages19
JournalJournal of Mathematical Analysis and Applications
Volume322
Issue number2
DOIs
Publication statusPublished - Oct 15 2006

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Keywords

  • Asymptotic behavior
  • Functional differential equation
  • Lyapunov exponent
  • Oscillation
  • Perron type theorem

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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