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On the relationship between two three-critical-point theorems. (English) Zbl 1242.58007
This paper deals with two recent results by Ricceri concerning the existence of multiple critical points for certain functionals defined on reflexive real Banach spaces. These abstract results are concerned with the following results: (i) existence of a local minimum and (ii) a minimax inequality together with a coercivity assumption that leads the existence of an interval of parameters such that a perturbed functional has a local, non-global minimum in the weak topology. In the paper under review it is argued that in both cases the hypotheses can be stated in terms of some elementary inequalities involving coercive sets of affine functions.

MSC:
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
35A16 Topological and monotonicity methods applied to PDEs
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