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 .
Definition 6.1.1 We say that a pair of subsets A, B of a Banach space E is a sandwich pair if every G ∈ C1 (E, ℝ) satisfying
and (PS)c for all c ∈ [b, a] has a critical point u with b ≤ G(u) ≤ a.
Example 6.1.2 If E = N ⊕ M 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 ...