The purpose of this chapter is to introduce the reader to linking methods used in variational problems. General references are Rabinowitz , Struwe , Chang , Benci , and Schechter ; see also Perera et al. . Our focus here will be the notion of homological linking, in particular, we will obtain pairs of critical points with nontrivial critical groups. Nonstandard geometries without a finite-dimensional closed loop will also be considered.
2.2 Minimax principle
Minimax principle originated in the work of Ljusternik and Schnirelmann  and is a useful tool for finding critical points of a functional. By Lemma 1.3.3, if c is a regular value, G satisfies (C)c, and ε > 0 is sufficiently small, ...