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arXiv · 1709.09867

The $1$-Yamabe equation on graph

Huabin Ge·Wenfeng Jiang
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Abstract

We study the following $1$-Yamabe equation on a connected finite graph $$Δ_1u+g\mathrm{Sgn}(u)=h|u|^{α-1}\mathrm{Sgn}(u),$$ where $Δ_1$ is the discrete $1$-Laplacian, $α>1$ and $g, h>0$ are known. We show that the above $1$-Yamabe equation always has a nontrivial solution $u\geq0$, $u\neq0$.

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Huabin Ge, Wenfeng Jiang. 2017-09-28. The $1$-Yamabe equation on graph. https://arxiv.org/abs/1709.09867

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