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.
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