A note on stability of impulsive scalar delay differential equations

• Main Authors: Teresa Faria, José Oliveira
• Format: Article
• Language: English
• Published: University of Szeged 2016-09-01
• Series: Electronic Journal of Qualitative Theory of Differential Equations
• Subjects: delay differential equation; impulses; yorke condition; global attractivity
• Online Access: http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=5287

For a class of scalar delay differential equations with impulses and satisfying a Yorke-type condition, criteria for the global asymptotic stability of the zero solution are established. These equations possess a non-delayed feedback term, which will be used to refine the general results on stability presented in recent literature. The usual requirements on the impulses are also relaxed. As an application, sufficient conditions for the global attractivity of a periodic solution for an impulsive periodic model are given.