Permanence in a class of delay differential equations with mixed monotonicity

In this paper we consider a class of delay differential equations of the form $\dot{x}(t)=\alpha (t) h(x(t-\tau), x(t-\sigma))-\beta(t)f(x(t))$, where $h$ is a mixed monotone function. Sufficient conditions are presented for the permanence of the positive solutions. Our results give also lower and u...

Full description

Saved in:
Bibliographic Details
Published in:Electronic journal of qualitative theory of differential equations 2018-01, Vol.2018 (53), p.1-21
Main Authors: Győri, István, Hartung, Ferenc, Mohamady, Nahed
Format: Article
Language:English
Subjects:
delay differential equations
mixed monotonicity
permanence
persistence
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper we consider a class of delay differential equations of the form $\dot{x}(t)=\alpha (t) h(x(t-\tau), x(t-\sigma))-\beta(t)f(x(t))$, 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.
ISSN:1417-3875
1417-3875
DOI:10.14232/ejqtde.2018.1.53