Mountain pass theorem with infinite discrete symmetry
Mountain pass theorem with infinite discrete symmetry
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 \textit{T. Bartsch} et al. [J. Reine Angew. Math. 419, 55--66 (1991; Zbl 0731.58016)] that deals with compact groups of symmetries.
- Osaka University Japan
Group-invariant bifurcation theory in infinite-dimensional spaces, Segal conjecture, 58E40, equivariant critical point theory, Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces, Variational aspects of group actions in infinite-dimensional spaces, Lusternik-Schnirelmann category, 55P91, mountain pass theorem, Equivariant homotopy theory in algebraic topology
Group-invariant bifurcation theory in infinite-dimensional spaces, Segal conjecture, 58E40, equivariant critical point theory, Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces, Variational aspects of group actions in infinite-dimensional spaces, Lusternik-Schnirelmann category, 55P91, mountain pass theorem, Equivariant homotopy theory in algebraic topology
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