| 有限图上高阶Yamabe型方程的非平凡解 |
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| 引用本文： | 刘春根,钟余友.有限图上高阶Yamabe型方程的非平凡解[J].数学物理学报(A辑),2021(1):39-45. |
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| 作者姓名： | 刘春根 钟余友 |
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| 作者单位： | 广州大学数学与信息科学学院 |
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| 基金项目： | 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。 |
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| 摘 要： | 该文研究了以下高阶Yamabe型方程Lm,pu?g|u|^p?2u=λf|u|α?2u在有限图上的非平凡正解的存在性,其中Lm,p是一个2m阶差分算子,它是一种p次(?Δ)^m算子更一般化,α≥p≥2,g>0和f>0是定义在G的所有顶点上的实函数,m≥1是一个整数.
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| 关 键 词： | 有限图 高阶Yamabe型方程 非平凡正解 |
Nontrivial Solution of High Order Yamabe-Type Equation on Finite Graph |
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| Liu Chungeng,Zhong Yuyou.Nontrivial Solution of High Order Yamabe-Type Equation on Finite Graph[J].Acta Mathematica Scientia,2021(1):39-45. |
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| Authors: | Liu Chungeng Zhong Yuyou |
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| Institution: | (School of Mathematics and Information Science,Guangzhou University,Guangzhou 510006) |
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| Abstract: | In this paper,we study the existence of nontrivial positive solution of the following high order Yamabe-type equation Lm,pu?g|u|^p?2u=λf|u|α?2u on a finite graph G,where Lm,p is a 2m-order difference operator which is a kind of p-th(?Δ)^m operator,α≥p≥2,g>0 and f>0 are real functions defined on all vertices of G,m≥1 is an integer.We show that the above equation always has a nontrivial solution u≥0 for some constantλ∈R. |
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| Keywords: | Finite graph High order Yamabe-type equation Nontrivial positive solution |
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