Geodesics with prescribed energy on static Lorentzian manifolds with convex boundary

By using some variational principles and the Ljusternik-Schnirelmann critic al point theory, we extend some previous results dealing with the existence and multiplicity of geodesics having prescribed energy joining a point wit h a line on static Lorentzian manifolds with convex boundary. Our technique s work also in the case of timelike and spacelike geodesics on manifolds wi th boundary and for a physically relevant class of spacetimes with non-smoo th boundary. (C) 2000 Elsevier Science B.V. All rights reserved.