On the linearization theorem for nonautonomous differential equations

Autor:	Rongting Wang, Donal O'Regan, Kit Ian Kou, Yonghui Xia
Rok vydání:	2015
Předmět:	Pure mathematics Picard–Lindelöf theorem Linearization General Mathematics Mathematical analysis Danskin's theorem Feedback linearization Brouwer fixed-point theorem Condensed Matter::Disordered Systems and Neural Networks Hartman–Grobman theorem Shift theorem Mean value theorem Mathematics
Zdroj:	Bulletin des Sciences Mathématiques. 139:829-846
ISSN:	0007-4497
Popis:	This paper presents an improvement of Palmer's linearization theorem in [10] . Palmer's linearization theorem extended the Hartman–Grobman theorem to the nonautonomous case. It requires two essential conditions: (i) the nonlinear term is bounded and Lipschitzian; (ii) the linear system as a whole possesses an exponential dichotomy. The main purpose of this paper is to weaken assumptions (i) and (ii). Also in this paper we prove that the topologically equivalent function H ( t , x ) in the linearization theorem is always Holder continuous (and has a Holder continuous inverse), so as a result we generalize and improve Palmer's linearization theorem.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::8e4176648815892ca4164b95456445eb https://doi.org/10.1016/j.bulsci.2014.12.005 Zobrazit plný text záznamu Full Text from ScienceDirect