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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A $p$-th Yamabe equation on graph
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by Huabin Ge PDF
Proc. Amer. Math. Soc. 146 (2018), 2219-2224 Request permission

Abstract:

Assume $\alpha \geq p>1$. Consider the following $p$-th Yamabe equation on a connected finite graph $G$: \begin{equation*} \Delta _p\varphi +h\varphi ^{p-1}=\lambda f\varphi ^{\alpha -1}, \end{equation*} where $\Delta _p$ is the discrete $p$-Laplacian, $h$ and $f>0$ are known real functions defined on all vertices. We show that the above equation always has a positive solution $\varphi$ for some constant $\lambda \in \mathbb {R}$.
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Additional Information
  • Huabin Ge
  • Affiliation: Department of Mathematics, Beijing Jiaotong University, Beijing 100044, People’s Republic of China
  • MR Author ID: 955742
  • Email: hbge@bjtu.edu.cn
  • Received by editor(s): December 11, 2016
  • Received by editor(s) in revised form: August 16, 2017
  • Published electronically: January 8, 2018
  • Additional Notes: The research is supported by National Natural Science Foundation of China under Grant No.11501027.
  • Communicated by: Goufang Wei
  • © Copyright 2018 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 146 (2018), 2219-2224
  • MSC (2010): Primary 34B35, 35B15, 58E30
  • DOI: https://doi.org/10.1090/proc/13929
  • MathSciNet review: 3767372