Asymptotically critical points and their multiplicity (Q701306)

The authors study multiplicity results for the critical points of a functional via topological information which ensures multiplicity of critical points for a sequence of approximating functionals. The main statement is Theorem 1.3 which states that the number of critical values of the functional in an interval is larger than the limsup of the relative categories of the sublevels (relatively to the same interval) of the approximating functionals. Some application to concrete problems as to the bounce trajectories between two given points in a billiard with perfectly elastic walls, possibly with a conservative field, are presented.