Boundedness and persistence of delay differential equations with mixed nonlinearity

Leonid Berezansky and Elena Braverman

Applied Mathematics and Computation, 2016, vol. 279, issue C, 154-169

Abstract: For a nonlinear equation with several variable delays x˙(t)=∑k=1mfk(t,x(h1(t)),⋯,x(hl(t)))−g(t,x(t)),where the functions fk increase in some variables and decrease in the others, we obtain conditions when a positive solution exists on [0, ∞), as well as explore boundedness and persistence of solutions. Finally, we present sufficient conditions when a solution is unbounded. Examples include the Mackey–Glass equation with non-monotone feedback and two variable delays; its solutions can be neither persistent nor bounded, unlike the well studied case when these two delays coincide.

Keywords: Nonlinear delay differential equations; A global positive solution; Persistent; permanent and unbounded solutions; Population dynamics models; Mackey–Glass equation (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:279:y:2016:i:c:p:154-169

DOI: 10.1016/j.amc.2016.01.015

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