Critical groups of pairs of critical points produced by linking subsets (Q1370990)

Linking of sets plays an important role in a wide variety of problems in the calculus of variations. The author proves near to \textit{M. Schechter} and \textit{K. Tintarev} [Bull. Soc. Math. Belg. 44, 249-261 (1992; Zbl 0785.58017)] a result about the critical points existence of \(F\in C(X,\mathbb{R})\) \((X\) is a Banach space) for homologically linking sets and shows that a certain critical group of each critical point is nontrivial.