Abstract
has at least ( G I (n + 1) distinct critical points (see [Kl, MA]; we refer also to Corollary (1.5) which is a generalization of this result). Consequently, the existence of a symmetry group G for the func- tionalf, in general defined on a Banach manifold, has a significant impact on the number of critical points. The problem of finding the best possible estimates for the number of orbits of critical points of an invariant func- tional was studied by many authors; for a I!,-action with p prime number, see [EL]; for S’-action, see [Bl, B2, CW2, CW3, FR2, R2]; for a non-free action, where Morse theory is applied, see [Pl, CWl, W]; see also [DA, FH, FRl]. This work is an attempt to give a general and explicit formula (cf. Theorem (1.3)) for the number of critical points of an invariant func- tional
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