On Palais' principle for nonsmooth functionals

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Abstract

If G is a compact Lie group acting linearly on a Banach space X and f is a G-invariant function on X, we provide some new versions of the so-called Palais’ principle of symmetric criticality for f : X → R, in the framework of non-smooth critical point theory. We apply the results to a class of quasi-linear PDEs associated with invariant functionals which are merely lower semi-continuous and thus could not be treated by previous non-smooth versions of the principle in the literature.
Original languageEnglish
Pages (from-to)3786-3804
Number of pages19
JournalNONLINEAR ANALYSIS
Volume74
Publication statusPublished - 2011

Keywords

  • Palais' principle

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