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Mountain pass theorem with infinite discrete symmetry. (English) Zbl 1375.58012

The Mountain Pass Theorem is one of the fundamental results of calculus of variations and nonlinear analysis, used to establish the existence of critical points (of higher index) with numerous applications in many areas of mathematics. The paper under review extends the classical formulation of this theorem to an equivariant setting, regarding functionals invariant under an infinite discrete group of symmetries. This is a modification of an earlier equivariant result of T. Bartsch et al. [J. Reine Angew. Math. 419, 55–66 (1991; Zbl 0731.58016)] that deals with compact groups of symmetries.

MSC:

58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
55P91 Equivariant homotopy theory in algebraic topology
58E09 Group-invariant bifurcation theory in infinite-dimensional spaces
58E40 Variational aspects of group actions in infinite-dimensional spaces

Citations:

Zbl 0731.58016
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Full Text: Euclid

References:

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