On Jack Hale's problem for impulsive systems

Autor(es)

Bonotto, E. M. ^[1] ; Gimenes, L. P. ^[2] ; Souto, G. M. ^[1]

Afiliação do(s) autor(es)

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

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

• Tipo de documento: Artigo Científico
• Fonte: Journal of Differential Equations; v. 259, n. 2, p. 642-665, JUL 15 2015.
• Citações Web of Science: 4

Resumo

An interesting problem of Jack Hale deals with the existence of a maximal compact invariant set in discrete dynamical systems. A solution for this problem is known for locally bounded dynamical systems. Following this line of research, we consider in this paper a class of systems whose continuous dynamics are interrupted by abrupt changes of state and we present sufficient conditions to obtain the existence of a maximal compact invariant set for a system in this class. We use the theory of asymptotic compactness to get the results. (C) 2015 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 12/20933-9 - Propriedades qualitativas de sistemas semidinâmicos impulsivos
• Beneficiário: Ginnara Mexia Souto
• Modalidade de apoio: Bolsas no Brasil - Doutorado
• Processo FAPESP: 12/16709-6 - Sistemas não autônomos com impulsos: sistemas convergentes e a Equação de Navier-Stokes
• Beneficiário: Everaldo de Mello Bonotto
• Modalidade de apoio: Auxílio à Pesquisa - Regular