Qualitative analysis of delay differential equations with non-instantaneous impulses: existence and controllability

In this paper, we mainly studied the non-instantaneous impulsive evolution equations with state-dependent delay under integral boundary conditions, and the evolution process of the non-instantaneous impulsive system was given. First, sufficient conditions were presented for the problem to have at least one solution when the related semigroup is compact. Second, the case when the associated semigroup is equicontinuous was presented by utilizing the theory of a semigroup. Third, the controllability of the considered problem was acquired via fixed point theory. In the end, examples were given to demonstrate the validity of the obtained results.