Hausdorff product measures and \(C^1\)-solution sets of abstract semilinear functional differential inclusions (Q2403339)

The paper studies a second-order semilinear differential inclusion with nonlocal conditions and set-valued impulses on a compact interval and in a separable Banach space. The linear part of the inclusion generates a strongly continuous cosine family. The nonlinear perturbation of the inclusion is given by a set-valued map which is weakly upper semicontinuous with convex, weakly compact values and satisfy a certain condition expressed in terms of the Hausdorff measure of noncompactness. Two results concerning the existence of \(C^1\) solutions of the problem considered are proved.