Symmetries, Morse Polynomials and Applications to Bifurcation Problems

In this paper-utilizing equivariant Mose theory for isolated critical orbits developed in [16] we study the versions of Morse identities under group actions.i.e.the global property of equivariant Morse the ory. Combining the concept of critical multiplicity we give a lower bound of the critical multiplicities for a class of invariant functionals. As applications we study the bifuractions of a class of equivariant potential op erators and generalize some results due to Benci and Pacella. Chang Rabinowitz, etc.