報告題目：Geometrically distinct solutions given by symmetries of variational
problems with the O(N) -symmetry
報告摘要：Abstract. For variational problems with O(N)-symmetry the existence of several geometrically distinct solutions has been shown by use of group theoretic approach in previous articles. It was done by a crafty choice of a family Hi ? O(N) subgroups such that the ?xed point subspaces EHi ? E of the action in a corresponding functional space are linearly independent, next restricting the problem to each EHi and using the Palais symmetry principle. In this work we give a thorough explanation of this approach showing a correspondence between the equivalence classes of such subgroups, partial orthogonal flags in RN, and unordered partitions of the number N. By showing that spaces of functions invariant with respect to di?erent classes of groups are linearly independent we prove that the amount of series of geometrically distinct solutions obtained in this way grows exponentially in N, in contrast to logarithmic, and linear growths of earlier papers.