Global attractivity in delay differential equations using a mixed monotone technique

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Abstract

We derive new sufficient conditions for global attractivity in nonlinear delay differential equations using a mixed monotone technique. The equations considered include the equation of the form d dt[x(t) - ax(t - τ)] = - μx(t) - bx(t - σ) + f(x(t - γ)), where a, b, μ, -, σ, and γ are nonnegative numbers such that a ε{lunate} [0, 1), b + μ > 0 and λ(1 - ae-λτ) = - μ - be- λσ has a negative root; moreover f(x) is a mixed monotone function, that is, f(x) = ω(x, x), where ω(x, y) is monotone decreasing in x and increasing in y. Our results are applied to some delay differential equations from mathematical biology.

Original languageEnglish
Pages (from-to)131-155
Number of pages25
JournalJournal of Mathematical Analysis and Applications
Volume152
Issue number1
DOIs
Publication statusPublished - 1990

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Global Attractivity
Delay Differential Equations
Monotone
Differential equations
Mathematical Biology
Monotone Function
Nonlinear Differential Equations
Non-negative
Roots
Sufficient Conditions
Form

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Global attractivity in delay differential equations using a mixed monotone technique. / Győri, I.

In: Journal of Mathematical Analysis and Applications, Vol. 152, No. 1, 1990, p. 131-155.

Research output: Contribution to journalArticle

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