Stability results for impulsive functional differential equations with infinite delay

Author(s)

Faria, Teresa ^{[1, 2]} ; Gadotti, Marta C. ^[3] ; Oliveira, Jose J. ^{[4, 5]}

Affiliation

^[1] Univ Lisbon, Fac Ciencias, Dept Matemat, P-1749016 Lisbon - Portugal

^[2] Univ Lisbon, Fac Ciencias, CMAF, P-1749016 Lisbon - Portugal

^[3] Univ Estadual Paulista, IGCE, Dept Matemat, BR-13506700 Rio Claro, SP - Brazil

^[4] Univ Minho, Escola Ciencias, Dept Matemat & Aplicacoes, P-4710057 Braga - Portugal

^[5] Univ Minho, Escola Ciencias, CMAT, P-4710057 Braga - Portugal

• Document type: Journal article
• Source: NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS; v. 75, n. 18, p. 6570-6587, DEC 2012.
• Web of Science Citations: 16

Abstract

For a family of differential equations with infinitive delay and impulses, we establish conditions for the existence of global solutions and for the global asymptotic and global exponential stabilities of an equilibrium point. The results are used to give stability criteria for a very broad family of impulsive neural network models with both unbounded distributed delays and bounded time-varying discrete delays. Most of the impulsive neural network models with delay recently studied are included in the general framework presented here. (C) 2012 Elsevier Ltd. All rights reserved. (AU)

• FAPESP's process: 10/12712-7 - Research plan on functional differential equations
• Grantee: Marta Cilene Gadotti
• Support Opportunities: Scholarships abroad - Research