Palais–Smale compactness condition
The Palais–Smale compactness condition, named after Richard Palais and Stephen Smale, is a hypothesis for some theorems of the calculus of variations. It is useful for guaranteeing the existence of certain kinds of critical points, in particular saddle points.
Source: Wikipedia — Palais–Smale compactness condition (CC BY-SA 4.0)