Asymptotically critical points and multiple elastic bounce trajectories

We study existence and multiplicity of elastic bounce trajectories with fixed end points in a general bounded open set of R^N, in presence of a force field. Assuming the existence of a "bounce free trajectory" touching the boundary we prove the existence of multiple families of "true bounce trajecories" bifurcating from the initial one, as a suitable par<meter varies. We use an approxumation scheme and a variational approach: to accomplish this we develop a notion of "asymptotically critical point" for a family of functionals.