Stability Analysis of Second Order Impulsive Differential Equations

• Qian Wen ^[1] ; JinRong Wang ^[1] ; Donal O'Regan ^[2]
  1. [1] Guizhou University

     Guizhou University

     China

     
  2. [2] National University of Ireland

     National University of Ireland

     Irlanda

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 2, 2022
• Idioma: inglés
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• Resumen

  • In this paper, we apply the strongly continuous cosine family of bounded linear operators to study the explicit representation of solutions for second order linear impulsive differential equations, and we give sufficient conditions for asymptotical stability of solutions. In addition we study the exponential stability of the linear perturbed problem. Existence and uniqueness of solutions of the initial value problem for nonlinear second order impulsive differential equations is obtained and we present Ulam–Hyers–Rassias stability results. Examples are provided to illustrate the applicability of our results.