数学物理学报 ›› 2021, Vol. 41 ›› Issue (1): 39-45.

• 论文 • 上一篇    下一篇

有限图上高阶Yamabe型方程的非平凡解

刘春根*(),钟余友()   

  1. 广州大学数学与信息科学学院 广州 510006
  • 收稿日期:2019-12-30 出版日期:2021-02-26 发布日期:2021-01-29
  • 通讯作者: 刘春根 E-mail:liucg@nankai.edu.cn;zhongyy@e.gzhu.edu.cn
  • 作者简介:钟余友, E-mail: zhongyy@e.gzhu.edu.cn
  • 基金资助:
    国家自然科学基金(11790271);广东省基础和应用基础研究项目(2020A1515011019);广州大学创新强效项目

Nontrivial Solution of High Order Yamabe-Type Equation on Finite Graph

Chungeng Liu*(),Yuyou Zhong()   

  1. School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006
  • Received:2019-12-30 Online:2021-02-26 Published:2021-01-29
  • Contact: Chungeng Liu E-mail:liucg@nankai.edu.cn;zhongyy@e.gzhu.edu.cn
  • Supported by:
    Supported by the NSFC(11790271);the Guangdong Basic and Applied Basic Research Foundation(2020A1515011019);the Innovation and Enhancement Project of Guangzhou University

摘要:

该文研究了以下高阶Yamabe型方程 在有限图上的非平凡正解的存在性,其中 $ {\cal L}_{m,p}$是一个 $2m $阶差分算子,它是一种 $ p$$ (-\Delta)^m$算子更一般化, $\alpha \geq p \geq 2 $$ g> 0$$f>0 $是定义在 $G $的所有顶点上的实函数, $m\ge 1 $是一个整数.

关键词: 有限图, 高阶Yamabe型方程, 非平凡正解

Abstract:

In this paper, we study the existence of nontrivial positive solution of the following high order Yamabe-type equation on a finite graph $ G$, where $ {\cal L}_{m, p}$ is a $ 2m$-order difference operator which is a kind of $ p$-th $ (-\Delta)^m$ operator, $ \alpha \geq p \geq 2$, $g>0 $ and $f>0 $ are real functions defined on all vertices of $G $, $ m\ge 1$ is an integer. We show that the above equation always has a nontrivial solution $u\ge 0 $ for some constant λ∈ ${\Bbb R} $.

Key words: Finite graph, High order Yamabe-type equation, Nontrivial positive solution

中图分类号: 

  • O176.3