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Topics in Critical Point Theory by Kanishka Perera, Martin Schechter

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6

Sandwich pairs

6.1 Introduction

The notion of sandwich pairs is a useful tool for finding critical points of a functional. It was introduced by Schechter [145, 146] and was based on the sandwich theorem for complementing subspaces by Schechter [137, 138] and Silva [150].

Definition 6.1.1  We say that a pair of subsets A, B of a Banach space E is a sandwich pair if every GC1 (E, ℝ) satisfying

images

and (PS)c for all c ∈ [b, a] has a critical point u with bG(u) ≤ a.

Example 6.1.2  If E = NM is a direct sum decomposition with N nontrivial and finite dimensional, then N, M form a sandwich pair. In fact, we will see in Section 6.3 that this ...

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