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Topics in Critical Point Theory by Kanishka Perera, Martin Schechter

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2

Linking

2.1 Introduction

The purpose of this chapter is to introduce the reader to linking methods used in variational problems. General references are Rabinowitz [129], Struwe [153], Chang [29], Benci [17], and Schechter [143]; see also Perera et al. [113]. 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 [85] 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, ...

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