A bisection algorithm for the numerical mountain pass (Q2474188)

This paper deals with constructive methods to seek critical points which are not minimizers for functionals defined on Hilbert spaces. The authors establish a constructive version of the Ambrosetti-Rabinowitz Mountain Pass Theorem, whose proof relies on an algorithm based on a bisection method depending on the topology of sublevels. Numerical applications and connections with the 3-body problem are also provided.