Copyright © 2010 Anna Maria Micheletti and Angela Pistoia. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Given that is a smooth compact and symmetric Riemannian -manifold, , we prove a multiplicity result for antisymmetric sign changing solutions of the problem in . Here if and if .