Impulsive differential inclusions involving evolution operators in separable Banach spaces - Benchohra, M.; Nieto, J. J.; Ouahab, A. (Ukrains’kyi Matematychnyi Zhurnal, 2012)
We present some results on the existence of mild solutions and study the topological structure of the sets of solutions forthe following first-order impulsive semilinear differential inclusions with initial and boundary conditions:$$y'(t) − A(t)y(t) \in F(t, y(t)) \text{for a.e.} t \in J\ \{t1,..., tm,...\},$$$$y(t^+_k) − y(t^−_k) = I_k(y(t^−_k)),\quad k = 1,...,$$$$y(0) = a$$and$$y'(t) − A(t)y(t) \in F(t, y(t)) \text{for a.e.} t \in J\ \{t1,..., tm,...\},$$$$y(t^+_k) − y(t^−_k) = I_k(y(t^−_k)),\quad k = 1,...,$$$$Ly = a,$$where $J = IR_+,\; 0 = t_0 < t_1