Boundness and Linearisation of a Class of Differential Equations with Piecewise Constant Argument

• Zou, Changwu ^[1] ; Xia, Yonghui ^[2] ; Pinto, Manuel ^[3] ; Shi, Jinlin ^[1] ; Bai, Yuzhen ^[4]
  1. [1] Fuzhou University

     Fuzhou University

     China

     
  2. [2] Zhejiang Normal University

     Zhejiang Normal University

     China

     
  3. [3] Universidad de Chile

     Universidad de Chile

     Santiago, Chile

     
  4. [4] Qufu Normal University

     Qufu Normal University

     China

     

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• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 18, Nº 2, 2019, págs. 495-531
• Idioma: inglés
• DOI: 10.1007/s12346-018-0297-9
• Enlaces
  • Texto completo
• Resumen

  • The differential equations with piecewise constant argument (DEPCAs, for short) is a class of hybrid dynamical systems (combining continuous and discrete). In this paper, under the assumption that the nonlinear term is partially unbounded, we study the bounded solution and global topological linearisation of a class of DEPCAs of general type. One of the purpose of this paper is to obtain a new criterion for the existence of a unique bounded solution, which improved the previous results. The other aim of this paper is to establish a generalized Grobman–Hartman-type theorem for the topological conjugacy between a nonlinear perturbation system and its linear system. The method is based on the new obtained criterion for bounded solution. The obtained results generalized and improved some previous papers. Some novel techniques are employed in the proof.

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