Sandwich Systems

Abstract

As we saw in Chap. 1, an important requirement for a linking pair is that they must separate the functional, i.e., they must satisfy

$$\displaystyle a_0 := \sup _{A} G \le b_0 := \inf _{B}G. $$

If a linking pair does not separate the functional, nothing can be said concerning a potential critical point. This raises the questions, “Is there anything one can do if one cannot find linking sets that separate the functional?” “Are there sets that can lead to critical sequences even though they do not separate the functional?” Fortunately, there are.