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 for the following first-order impulsive semilinear differential inclusions with initial and boundary conditions: y’(t) − A(t)y(t) F(t, y(t)) for a.e. t J {t1,..., tm,...}, y(t^+_k) − y(t^−_k) = I_k(y(t^−_k)),k = 1,..., y(0) = a and y’(t) − A(t)y(t) F(t, y(t)) for a.e. t J {t1,..., tm,...}, y(t^+_k) − y(t^−_k) = I_k(y(t^−_k)),k = 1,..., Ly = a, where J = IR_+, 0 = t_0 < t_1