Sandwich systems
The paper under review deals with some interesting and modern topics concerning the qualitative analysis of energy functionals that are naturally associated to various classes of stationary problems. If the energy functional \(G\) is bounded from below, one can show that there is a Palais-Smale sequence \((u_n)\) satisfying \(G(u_n) \rightarrow a\) and \(G'(u_n)\rightarrow 0\), where \( a = \inf G\). If the sequence has a convergent subsequence, this will produce a minimum. However, when the functional is not semibounded, the matter is more complicated and can have different features. That is why different devices must be used according to the various difficulties that can occur (mountain pass geometry, saddle point structure, linking, restriction to the Nehari manifold, Benci-Rabinowitz theorem, etc.). In the present paper it is developed an approach that produces Cerami-type sequences for functionals which are not semibounded. They are not quite Cerami sequences, but they are just as effective in many applications, as pointed out in the last part of this paper.
scientific article; zbMATH DE number 6125368