Topological structure of the solutions set of impulsive semilinear differential inclusions with nonconvex right-hand side (Q2516271)

The authors consider the following first-order impulsive evolution inclusion with initial conditions: \[ \begin{aligned} & y'(t)-Ay(t)\in F(t,x(t)) \text{ for } \text{a.e.}\,\, t\in J\setminus\{t_1, t_2, \ldots, t_m\},\\ & \Delta y_{It=t_{k}}:=y(t_k^+)-y(t_k^-)=I_k(y(t_k^-)), ~~ k=1,2, \ldots, m,\\ &y(0)=a, \end{aligned} \] where \(0=t_0<t_1<\ldots<t_m<t_{m+1}=b,\) \(J=[0,b],\) \(F: J\times E\to {\mathcal P}(E)\) is a multifunction, the operator \(A\) is the infinitesimal generator of a \(C_0\)-semigroup \(\{T(t)\}_{t\geq 0},\) and \(I_k \in C(E,E)\) \((k = 1,\ldots ,m).\) The topological structures of the solution set are investigated, where the right-hand side is not necessarily convex valued.