Stability of functional differential equations with variable impulsive perturbations via generalized ordinary differential equations

Author(s)

Afonso, S. M. ^[1] ; Bonotto, E. M. ^[1] ; Federson, M. ^[1] ; Gimenes, L. P. ^[2]

Affiliation

^[1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, BR-13560970 Sao Carlos, SP - Brazil

^[2] Univ Estadual Maringa, Dept Matemat, BR-87020900 Maringa, Parana - Brazil

• Document type: Journal article
• Source: BULLETIN DES SCIENCES MATHEMATIQUES; v. 137, n. 2, p. 189-214, MAR 2013.
• Web of Science Citations: 13

Abstract

We consider a class of functional differential equations with variable impulses and we establish new stability results. We discuss the variational stability and variational asymptotic stability of the zero solution of a class of generalized ordinary differential equations where our impulsive functional differential equations can be embedded and we apply that theory to obtain our results, also using Lyapunov functionals. (C) 2012 Elsevier Masson SAS. All rights reserved. (AU)

• FAPESP's process: 08/04159-6 - Topological dynamics in Kurzweil equations and applications to retarded functional differential equations
• Grantee: Suzete Maria Silva Afonso
• Support type: Scholarships in Brazil - Doctorate
• FAPESP's process: 08/02879-1 - Functional differential equations with delay and impulses
• Grantee: Márcia Cristina Anderson Braz Federson
• Support type: Regular Research Grants
• FAPESP's process: 10/08994-7 - Non-autonomous semidynamical systems with impulses
• Grantee: Everaldo de Mello Bonotto
• Support type: Regular Research Grants