Positive Periodic Solutions of Systems of First Order Ordinary Differential Equations

Donal O’Regan, Haiyan Wang

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

Consider the n-dimensional nonautonomous system ẋ(t) = A(t)G(x(t)) − B(t)F(x(t − τ(t))) Let u = (u1,…,un),(Formula Presented.). Under some quite general conditions, we prove that either F0 = 0 and F = ∞, or F0 = ∞ and F = 0, guarantee the existence of positive periodic solutions for the system for all λ > 0. Furthermore, we show that F0 = F = 0, or F = F = ∞ guarantee the multiplicity of positive periodic solutions for the system for sufficiently large, or small λ, respectively. We also establish the nonexistence of the system when either F0 and F > 0, or F0 and F, < for sufficiently large, or small λ, respectively. We shall use fixed point theorems in a cone.

Original languageEnglish (US)
Pages (from-to)310-325
Number of pages16
JournalResults in Mathematics
Volume48
Issue number3-4
DOIs
StatePublished - Nov 1 2005

Keywords

  • existence
  • fixed point theorem
  • positive periodic solutions

ASJC Scopus subject areas

  • Mathematics (miscellaneous)
  • Applied Mathematics

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