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- W2912298464 abstract "Given any closed Riemannian manifold $(M,g)$ we use the Lyapunov-Schmidt finite-dimensional reduction method and the classical Morse and Lusternick-Schnirelmann theories to prove multiplicity results for positive solutions of a subcritical Yamabe type equation on $(M,g)$. If $(N,h)$ is a closed Riemannian manifold of constant positive scalar curvature we obtain multiplicity results for the Yamabe equation on the Riemannian product $(Mtimes N , g + ve^2 h )$, for $ve >0$ small. For example, if $M$ is a closed Riemann surface of genus ${bf g}$ and $(N,h) = (S^2 , g_0)$ is the round 2-sphere, we prove that for $ve >0$ small enough and a generic metric $g$ on $M$, the Yamabe equation on $(Mtimes S^2 , g + ve^2 g_0 )$ has at least $2 + 2 {bf g}$ solutions." @default.
- W2912298464 created "2019-02-21" @default.
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- W2912298464 creator A5074951638 @default.
- W2912298464 date "2018-12-10" @default.
- W2912298464 modified "2023-09-27" @default.
- W2912298464 title "Solutions of the Yamabe Equation By Lyapunov-Schmidt Reduction" @default.
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