A p-th Yamabe equations on graph

Huabin Ge

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arXiv · 1611.04906

A p-th Yamabe equations on graph

Huabin Ge

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Abstract

Assume $\alpha\geq p>1$. Consider the following $p$-th Yamabe equation on a connected finite graph $G$: $$\Delta_p\varphi+h\varphi^{p-1}=\lambda f\varphi^{\alpha-1},$$ where $\Delta_p$ is the discrete $p$-Laplacian, $h$ and $f>0$ are fixed real functions defined on all vertices. We show that the above equation always has a positive solution $\varphi$ for some constant $\lambda\in\mathds{R}$.

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Huabin Ge. 2016-11-15. A p-th Yamabe equations on graph. https://arxiv.org/abs/1611.04906

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