On stability for  impulsive  delay differential equations and application to a periodic  Lasota-Wazewska model

Teresa  Faria; José J.  Oliveira

doi:10.3934/dcdsb.2016055

Article Contents

2016, Volume 21, Issue 8: 2451-2472. Doi: 10.3934/dcdsb.2016055

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On stability for impulsive delay differential equations and application to a periodic Lasota-Wazewska model

Teresa Faria^1, and
José J. Oliveira^2,

1.
Departamento de Matematica and CMAF-CIO, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, 1749-016 Lisboa
2.
CMAT and Departamento de Matemática e Aplicações, Escola de Ciências, Universidade do Minho, Campus de Gualtar, 4710-057 Braga

Received: July 2015

Revised: June 2016

Published: October 2016

Abstract / Introduction Related Papers Cited by

Abstract

We consider a class of scalar delay differential equations with impulses and satisfying an Yorke-type condition, for which some criteria for the global stability of the zero solution are established. Here, the usual requirements about the impulses are relaxed. The results can be applied to study the stability of other solutions, such as periodic solutions. As an illustration, a very general periodic Lasota-Wazewska model with impulses and multiple time-dependent delays is addressed, and the global attractivity of its positive periodic solution analysed. Our results are discussed within the context of recent literature.

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Mathematics Subject Classification: 34K45, 34K25, 92D25.

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