The authors consider a second order differential inclusion subject to a set of nonlinear boundary constraints
where are given homeomorphisms and are continuous, moreover
where . Their main existence result, Theorem 2.2, is proved by means of the topological transversality method of Granas based on the existence of a priori bounds for the solutions of the above boundary value problem which is suitably modified to deal with the impulsive nature of the problem. Two motivating examples involving impulses are presented.