Abstract
We consider functionals that are invariant under the action of an arbitrary group of symmetries and have the mountain pass geometry, and introduce a suitable notion of genus which allows computation of lower bounds for the Morse indices of critical orbits at corresponding minimax values. Via a Borsuk-Ulam type property, we relate these critical values to those which are relevant for obtaining multiplicity results for perturbed symmetric problems. This allows us to obtain good estimates for their growth, which are useful in applications, and extends previous results of Bahri and Lions and Tanaka for even functionals to more general group actions.
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Clapp, M. (2002). Morse Indices at Mountain Pass Orbits of Symmetric Functionals. In: Benci, V., Cerami, G., Degiovanni, M., Fortunato, D., Giannoni, F., Micheletti, A.M. (eds) Variational and Topological Methods in the Study of Nonlinear Phenomena. Progress in Nonlinear Differential Equations and Their Applications, vol 49. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0081-9_1
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DOI: https://doi.org/10.1007/978-1-4612-0081-9_1
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