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The Morse index of a saddle point. (English) Zbl 0732.58011
This paper offers a way to estimate the Morse index of a critical point obtained via a min-max technique. The basic idea is that if a critical point has Morse index m then the m-th homology group of a pair of level sets should be nontrivial. Thus the problem is reduced to constructing critical points for which these groups do not vanish. The main trick is then a clever notion of link with a corresponding min-max technique which will offer the desired result. The knowledge of the Morse index is often useful in proving multiplicity results as the author does in Theorem 2.2 when a new proof to an old multiplicity result is given.

58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
49J35 Existence of solutions for minimax problems