I am trying to understand one of the most important concept in Calculs of Variations. I have often heard that the change of topology implies the existence of a critical point. In this context, critical (subcritical) levels have a fundamental role. I don't know something more.
Could anyone please explain me (also intuitively) how critical levels are related to critical points of a functional? What is a critical level of minimax type?
Some examples or references will be appreciated, too. Thank you in advance!