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Controllability and Hyers--Ulam stability of impulsive second order abstract damped differential system
Akbar Zada,Luqman Alam,Jiafa Xu
Keywords:Damped differential equation; Impulsive system; Controllability; $\beta$--Hyers--Ulam--Rassias stability
Abstract:
      In this paper, we consider system of damped second order abstract impulsive differential equations to investigate its controllability and Hyers--Ulam stability. For our results about the controllability, we utilized the theory of strongly continuous cosine families of linear operators combined with Sadovskii fixed point theorem. In addition, different types of Hyers--Ulam stability is established with the help of Gr\"{o}nwall"s type inequality and Lipschitz conditions. At last, we give an example of damped wave equation which outline the application of our principle results.