Solvability of the equation Δ_{𝑔}𝑢+𝑆̃𝑢^{𝜎}=𝑆𝑢 on manifolds

Tang, Jun Jie

doi:10.1090/S0002-9939-1994-1174496-1

Solvability of the equation $\Delta _ gu+\tilde {S}u^ \sigma =Su$ on manifolds
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Proc. Amer. Math. Soc. 121 (1994), 83-92 Request permission

Abstract:

For the negative Yamabe invariant and $\tilde S \leq 0$, we obtain that the equation ${\Delta _g}u + \tilde S{u^\sigma } = Su$ has a positive solution if and only if the supremum of the Yamabe invariant over all smooth coverings of the 0-level set of $\tilde S$ is positive.

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