Nontrivial solutions of operator equations and Morse indices of critical points of min-max type. (English) Zbl 0667.47036

There is proved a series of theorems concerning the Morse indices of critical points of min-max type. In particular, three new proofs of the Amann-Zehnder theorem are given. The results obtained here can be used to establish the existence of multiple solutions of certain semilinear boundary value problems.
Reviewer: P.Drabek


47J05 Equations involving nonlinear operators (general)
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
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