### 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 language | English |
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Pages (from-to) | 131-155 |

Number of pages | 25 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 152 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1990 |

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### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

### Cite this

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

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Global attractivity in delay differential equations using a mixed monotone technique

AU - Győri, I.

PY - 1990

Y1 - 1990

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=38249016217&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38249016217&partnerID=8YFLogxK

U2 - 10.1016/0022-247X(90)90096-X

DO - 10.1016/0022-247X(90)90096-X

M3 - Article

AN - SCOPUS:38249016217

VL - 152

SP - 131

EP - 155

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 1

ER -