Journal
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
Volume 149, Issue 10, Pages 4419-4429Publisher
AMER MATHEMATICAL SOC
DOI: 10.1090/proc/15548
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- Fondo Sectorial SEP-CONACYT [A1-S-45886]
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For a closed cohomogeneity one Riemannian manifold of dimension n ≥ 3 with positive Ricci curvature, infinite nodal solutions for certain equations can be proven to exist. Specifically, for a positive Einstein manifold of cohomogeneity one or fibered over such a manifold, the existence of infinite nodal solutions for the Yamabe equation can be established with a prescribed number of connected components of its nodal domain.
We consider a closed cohomogeneity one Riemannian manifold (M-n, g) of dimension n >= 3. If the Ricci curvature of M is positive, we prove the existence of infinite nodal solutions for equations of the form -Delta(g)u + lambda u = lambda u(q) with lambda > 0, q > 1. In particular for a positive Einstein manifold which is of cohomogeneity one or fibers over a cohomogeneity one Einstein manifold we prove the existence of infinite nodal solutions for the Yamabe equation, with a prescribed number of connected components of its nodal domain.
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