|
| 摘要: |
| 本文研究了cigar孤立子$(\mathbb{R}^2,g,f)$上漂移Laplace算子的多项式算子的加权Dirichlet特征值问题：
$$
\left\{\begin{array}{ll}
\displaystyle L^2_\phi u-a L_{\phi}u+bu=\lambda \rho u,& u \in \Omega\\[8pt]
u=\displaystyle\frac{\partial{u}}{\partial{v}}=0,& u \in \partial{\Omega}\\
\end{array}\right.
$$
其中$\rho$是$\Omega$上的正连续函数,$v$是$\partial \Omega $的单位外法向量,$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:国家自然科学基金项目（面上项目，重点项目，重大项目） |
|
| Inequalities for eigenvalues of polynomial operator of the drifting Laplacian on the cigar soliton |
|
Sun He-jun
|
| Abstract: |
| In this paper, we investigate the weighted Dirichlet eigenvalue problem of polynomial operator of the drifting Laplacian on the cigar soliton $(\mathbb{R}^2, g, \phi)$ as follows
$$
\left\{\begin{array}{ll}
\displaystyle L^2_\phi u-a L_{\phi}u+bu=\lambda \rho u,& u \in \Omega\\[8pt]
u=\displaystyle\frac{\partial{u}}{\partial{v}}=0,& u \in \partial{\Omega}\\
\end{array}\right.
$$
where $\rho$ is a positive continuous function on $\Omega$, $v$ denotes the outward unit normal to the boundary $\partial \Omega $, and $a,b$ are two nonnegative constants. We establish some universal inequalities for eigenvalues of this problem. |
| Key words: drifting Laplacian cigar soliton eigenvalue |
