New Results on Linearization of Differential Equations with Piecewise Constant Argument

• Huang, Hai ^[1] ; Yong-Hui, Xia ^[2]
  1. [1] East China Normal University

     East China Normal University

     China

     
  2. [2] Zhejiang Normal University

     Zhejiang Normal University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 19, Nº 1, 2020
• Idioma: inglés
• DOI: 10.1007/s12346-020-00353-w
• Enlaces
  • Texto completo
• Resumen

  • In this work, we give a version of Grobman–Hartman theorem for the nonautonomous differential equations with piecewise constant argument of generalized type when the nonlinear term is unbounded and its linear system partially satisfies α-exponential dichotomy. More specifically, we divide the linear system into three subsystems, one of the subsystems is not necessary to admit α-exponential dichotomy. It was assumed that the whole linear system admits exponential dichotomy in Pinto and Robledo (Z Anal Anwend 37:101–126, 2018), Zou and Shi (J Appl Anal Comput 7(1):309–333, 2017) and Zou et al. (Qual Theory Dyn Syst 18:495–531, 2019). Thus, we extend and improve the previous results in the literature. Moreover, we prove that the conjugated function H(t, x) is also ω-periodic when the systems are ω-periodic.

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