On the impulsive Dirichlet problem for second-order differential inclusions

Solutions in a given set of an impulsive Dirichlet boundary value problem are investigated for second-order differential inclusions. The method used for obtaining the existence and the localization of a solution is based on the combination of a fixed point index technique developed by ourselves earlier with a bound sets approach and Scorza-Dragoni type result. Since the related bounding (Liapunov-like) functions are strictly localized on the boundaries of parameter sets of candidate solutions, some trajectories are allowed to escape from these sets.