A note on solutions of Yamabe-type equations on products of spheres

Abstract

We consider Yamabe-type equations on the Riemannian product of constant curvature metrics on ${\text{S}}^n\times {\text{ S}}^n$, and study solutions which are invariant by the cohomogeneity one diagonal action of $O(n+1)$. We obtain multiplicity results for both positive and nodal solutions. In particular we prove the existence of nodal solutions of the Yamabe equation on these products which depend non-trivially on both factors

12 pages

References in corpus (3)

• Symmetry and Asymmetry: The Method of Moving Spheres
• Multiplicity of solutions to the Yamabe problem on collapsing Riemannian submersions
• Nonexistence and multiplicity of solutions to elliptic problems with supercritical exponents