TY - JOUR AU - M. Benchohra AU - J. J. Nieto AU - A. Ouahab PY - 2012/07/25 Y2 - 2024/03/29 TI - Impulsive differential inclusions involving evolution operators in separable Banach spaces JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 64 IS - 7 SE - Research articles DO - UR - https://umj.imath.kiev.ua/index.php/umj/article/view/2625 AB - 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