Periodic solutions of angiogenesis models with time lags

P. Amster, L. Berezansky, L. Idels

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


To enrich the dynamics of mathematical models of angiogenesis, all mechanisms involved are time-dependent. We also assume that the tumor cells enter the mechanisms of angiogenic stimulation and inhibition with some delays. The models under study belong to a special class of nonlinear nonautonomous systems with delays. Explicit sufficient and necessary conditions for the existence of the positive periodic solutions were obtained via topological methods. Numerical examples illustrate our findings. Some open problems are presented for further studies.

Original languageEnglish
Pages (from-to)299-311
Number of pages13
JournalNonlinear Analysis: Real World Applications
Issue number1
StatePublished - 1 Feb 2012


  • A priori estimates
  • Angiogenesis
  • Existence of positive periodic solutions
  • LeraySchauder degree methods
  • Nonlinear nonautonomous delay differential equations
  • Second order Liénard type equation

ASJC Scopus subject areas

  • Analysis
  • General Engineering
  • Economics, Econometrics and Finance (all)
  • Computational Mathematics
  • Applied Mathematics


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