Multiple critical points of perturbed symmetric functionals

Rabinowitz, Paul H.

doi:10.1090/S0002-9947-1982-0662065-5

Multiple critical points of perturbed symmetric functionals
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by Paul H. Rabinowitz

Trans. Amer. Math. Soc. 272 (1982), 753-769

DOI: https://doi.org/10.1090/S0002-9947-1982-0662065-5

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Abstract:

Variational problems which are invariant under a group of symmetries often possess multiple solutions. This paper studies the effect of perturbations which are not small and which destroy the symmetry for two classes of such problems and shows how multiple solutions persist despite the perturbation.

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On

versions of the Borsuk-Ulam Theorem