Existence of solutions for semi-linear abstract differential equations with not instantaneous impulses

Variational approach to non-instantaneous impulsive nonlinear differential equations

“…The existence of solutions of non-instantaneous impulsive problem has been studied via some approaches, such as fixed point theory and theory of analytic semigroup, see, for example, [5,7,11,12]. Recently, the variational structure of non-instantaneous impulsive linear problem has been developed in [3].…”

Existence Results for Fractional Integro-Differential Equations with Fractional Order Non-instantaneous Impulsive Conditions

“…The non-instantaneous impulsive systems are more suitable to study the dynamics of evolution processes in pharmacotheraphy. The existence of solutions for non-instantaneous impulsive fractional/ integer order differential equations has also been studied [4,6,10,26,29,30].…”

Periodic boundary value problems for fractional semilinear integro-differential equations with non-instantaneous impulses

“…In [18][19][20], differential equations are all integer order, the linear operator A is independent of t, and the semigroup is compact. In [24][25][26], the linear operator A is independent of t. In this paper, we consider the existence of mild solutions for the fractional differential equations (1.1) under the conditions of the compact and noncompact semigroup; meanwhile, the linear operator A(t) is dependent on t. Therefore, the results presented in this paper improve and generalize the main results in [18][19][20][24][25][26] by using a different method.…”

“…The differential equations with non-instantaneous impulses of the following form were initially investigated by the authors in [18,19]:…”