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 .
Anna Maria Micheletti. Angela Pistoia. "On the Existence of Nodal Solutions for a Nonlinear Elliptic Problem on Symmetric Riemannian Manifolds." Int. J. Differ. Equ. 2010 (SI3) 1 - 11, 2010. https://doi.org/10.1155/2010/432759