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| 边界条件中带有谱参数的不连续Sturm-Liouville算子的特征值问题 | |
| 引用本文： | 姚斯琴,孙炯. 边界条件中带有谱参数的不连续Sturm-Liouville算子的特征值问题[J]. 应用数学, 2012, 25(1): 12-19 |
| 作者姓名： | 姚斯琴 孙炯 |
| 作者单位： | 内蒙古大学数学科学学院,内蒙古呼和浩特,010021 |
| 基金项目： | 国家自然科学基金资助项目 |
| 摘 要： | 本文研究了具有转移条件且边界条件含特征参数的Sturm-Liouville算子L的特征值问题.首先,使用微分算子谱分析经典的方法,得到λ是该边值问题的特征值的充要条件,证明了该边值问题最多有可数个实的特征值、没有有限值的聚点.其次,通过渐近估计证得,所研究的Sturm-Liouville算子L有可数个离散的特征值且下方有界. |
| 关 键 词： | Sturm-Liouville算子 转移条件 含参数边界条件 渐近式 特征值 |
Sturm-Liouville Operators with Transmission Conditions and Eigenparameter-dependent Boundary Conditions |
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| YAO Siqin , SUN Jiong. Sturm-Liouville Operators with Transmission Conditions and Eigenparameter-dependent Boundary Conditions[J]. Mathematica Applicata, 2012, 25(1): 12-19 | |
| Authors: | YAO Siqin SUN Jiong |
| Affiliation: | (School of Mathematical Sciences,Inner Mongolia University,Hohhot 010021,China) |
| Abstract: | In this paper,we investigate properties of eigenvalues of the Sturm-Liouville operators with transmission conditions and eigenparameter-dependent boundary conditions.Firstly,by means of studying the operator itself,we obtain the necessary and sufficient conditions for λ being a eigenvalue,and then prove that the eigenvalues of the boundary-value problem are bounded below,and they are countably infinite and can cluster only at ∞. |
| Keywords: | Sturm-Liouville operator Transmission condition Eigenparameter-dependent boundary condition Asymptotic approximation Eigenvalue |
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