| 摘要: |
| 本文研究了cigar孤立子R2,g,f上漂移Laplace算子的多项式算子的加权Dirichlet特征值问题：{Lϕ2u-aLϕu+bu=λρu,u∈Ω u=∂u/∂v=0,u∈∂Ω.其中ρ是Ω上的正连续函数,v是∂Ω的单位外法向量,a,b是两个非负常数.我们建立了该问题的一些特征值不等式. |
| 关键词: 漂移Laplace算子|Cigar孤立子|特征值 |
| DOI： |
| 分类号:O175.9;O186.1 |
| 基金项目:Supported by National Natural Science Foundation of China (11001130, 12272062); Fundamental Research Funds for the Central Universities (30917011335). |
|
| INEQUALITIES FOR EIGENVALUES OF POLYNOMIAL OPERATOR OF THE DRIFTING LAPLACIAN ON THE CIGAR SOLITON |
|
YUAN Yuan, SUN He-jun
|
|
School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210014, China
|
| Abstract: |
| In this paper, we investigate the weighted Dirichlet eigenvalue problem of polynomial operator of the drifting Laplacian on the cigar soliton (R2,g,ϕ) as follows {Lϕ2u-aLϕu+bu=λρu,u∈Ω u=∂u/∂v=0,u∈∂Ω where ρ is a positive continuous function on Ω, v denotes the outward unit normal to the boundary ∂Ω, and a, b are two nonnegative constants. We establish some universal inequalities for eigenvalues of this problem. |
| Key words: drifting Laplacian|Cigar soliton|eigenvalue |
