Discontinuous local semiflows for Kurzweil equations leading to LaSalle's invariance principle for differential systems with impulses at variable times

Author(s)

Afonso, S. M. ^[1] ; Bonotto, E. M. ^[1] ; Federson, M. ^[1] ; Schwabik, S. ^[1]

Affiliation

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

• Document type: Journal article
• Source: Journal of Differential Equations; v. 250, n. 7, p. 2969-3001, APR 1 2011.
• Web of Science Citations: 19

Abstract

In this paper, we consider an initial value problem for a class of generalized ODEs, also known as Kurzweil equations, and we prove the existence of a local semidynamical system there. Under certain perturbation conditions, we also show that this class of generalized ODEs admits a discontinuous semiflow which we shall refer to as an impulsive semidynamical system. As a consequence, we obtain LaSalle's invariance principle for such a class of generalized ODEs. Due to the importance of LaSalle's invariance principle in studying stability of differential systems, we include an application to autonomous ordinary differential systems with impulse action at variable times. (C) 2011 Elsevier Inc. 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 Opportunities: Scholarships in Brazil - Doctorate
• FAPESP's process: 08/02879-1 - Functional differential equations with delay and impulses
• Grantee: Márcia Cristina Anderson Braz Federson
• Support Opportunities: Regular Research Grants