Eventually positive solutions of first order nonlinear differential equations with a deviating argument

T. Sakamoto, S. Tanaka

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

The following first order nonlinear differential equation with a deviating argument, is considered, where α > 0, α ≠ 1, p ∈ C[t0; ∞), p(t) > 0 for t ≧ t0, τ ∈ C[t0; ∞), limt→∞τ(t) = ∞, τ(t) < t for t ≧ t0. Every eventually positive solution x(t) satisfying limt→∞x(t) ≧ 0. The structure of solutions x(t) satisfying limt→∞x(t) > 0 is well known. In this paper we study the existence, nonexistence and asymptotic behavior of eventually positive solutions x(t) satisfying limt→∞x(t) = 0.

Original languageEnglish
Pages (from-to)17-33
Number of pages17
JournalActa Mathematica Hungarica
Volume127
Issue number1
DOIs
Publication statusPublished - 2010 Apr
Externally publishedYes

Keywords

  • Asymptotic behavior
  • Deviating argument
  • Eventually positive solution

ASJC Scopus subject areas

  • Mathematics(all)

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