Differentiability of Semi-Flow for Impulsive Evolution Equation with State-Dependent Delay

• Weifeng Ma ^[1] ; Yongxiang Li ^[2]
  1. [1] Shaanxi Xueqian Normal University

     Shaanxi Xueqian Normal University

     China

     
  2. [2] Northwest Normal University

     Northwest Normal University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº Extra 1, 2024
• Idioma: inglés
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• Resumen

  • In this paper, we study the impulsive evolution equation with state-dependent delay by the theory of operator semigroup in Banach spaces. Under conditions that both nonlinearity and impulsive functions are Lipschitz continuous, we obtain the existence and uniqueness results of mild solution. Furthermore, we prove the differentiability of a semi-flow defined by a continuously differentiable solution operator under the appropriate condition.