Boundedness and persistence of delay differential equations with mixed nonlinearity

Leonid Berezansky, Elena Braverman

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


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.

Original languageEnglish
Pages (from-to)154-169
Number of pages16
JournalApplied Mathematics and Computation
StatePublished - 10 Apr 2016


  • A global positive solution
  • Mackey-Glass equation
  • Nonlinear delay differential equations
  • Persistent
  • Population dynamics models
  • permanent and unbounded solutions

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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