Permanence in a class of delay differential equations with mixed monotonicity

I. Győri, F. Hartung, Nahed A. Mohamady

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2 Citations (Scopus)

Abstract

In this paper we consider a class of delay differential equations of the form ẋ(t) = α(t)h(x(t − τ), x(t − σ)) − β(t) f (x(t)), where h is a mixed monotone function. Sufficient conditions are presented for the permanence of the positive solutions. Our results give also lower and upper estimates of the limit inferior and the limit superior of the solutions via a special solution of an associated nonlinear system of algebraic equations. The results are generated to a more general class of delay differential equations with mixed monotonicity.

Original languageEnglish
Article number53
JournalElectronic Journal of Qualitative Theory of Differential Equations
Volume2018
DOIs
Publication statusPublished - Jan 1 2018

Fingerprint

Permanence
Delay Differential Equations
Monotonicity
Differential equations
Monotone Function
Algebraic Equation
Positive Solution
Nonlinear Systems
Nonlinear systems
Sufficient Conditions
Estimate
Class
Form

Keywords

  • Delay differential equations
  • Mixed monotonicity
  • Permanence
  • Persistence

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

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AU - Hartung, F.

AU - Mohamady, Nahed A.

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AB - In this paper we consider a class of delay differential equations of the form ẋ(t) = α(t)h(x(t − τ), x(t − σ)) − β(t) f (x(t)), where h is a mixed monotone function. Sufficient conditions are presented for the permanence of the positive solutions. Our results give also lower and upper estimates of the limit inferior and the limit superior of the solutions via a special solution of an associated nonlinear system of algebraic equations. The results are generated to a more general class of delay differential equations with mixed monotonicity.

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