Existence of semi linear impulsive neutral evolution inclusions with infinite delay in Frechet spaces (Q515419)

In this paper, the authors study the existence of mild solutions to the following first order impulsive differential inclusions with infinite delay in a Banach space \(E\): \[ \begin{aligned} \frac{d}{dt}(y(t)-g(t,y_t)) &\in A(t)y(t) + F(t,y(t)), \quad t\in [0,\infty)\backslash\{t_k : k \in \mathbb{N}\}, \\ \Delta y(t_k) &= I_k(y(t_k^-)), \quad k\in \mathbb{N}, \\ y_0= \phi; \end{aligned} \] where \(\{A(t)\}_{t\in[0,\infty)}\) is a family of closed linear operators generating an evolution system \(\{U(t,x)\}\) and \(F\) is a \(L^1_{\mathrm{loc}}\)-Carathéodory multi-valued map with convex, compact values and satisfying a locally Lipschitz type condition with respect to the second variable.