微分算子第二特征值的上界不等式  

The Inequality of the Upper Bound of Second Eigenvalue for the Differential Operator

作　　者：赵晓苏[1] 钱椿林[1] ZHAO Xiaosu;QIAN Chunlin(Department of Mathematics and Physics,Suzhou Vocational University,Suzhou 215104,China)

机构地区：[1]苏州市职业大学数理部,江苏苏州215104

出　　处：《苏州市职业大学学报》2017年第3期43-49,共7页Journal of Suzhou Vocational University

摘　　要：考虑微分算子第二特征值的上界不等式的问题。利用试验函数、多次分部积分、Rayleigh定理、Schwarz不等式与Young不等式等,得到用微分算子的第一个特征值来估计第二个特征值的不等式,其不等式在物理学和力学中应用广泛,在微分方程的理论研究中有重要的作用。This paper considers the inequality of the upper bound of second eigenvalue for the differentialoperator.The inequality of the upper bound of second eigenvalue is deduced from first eigenvalue by using testingfunction,Rayleigh theorem,multiple partial integration,Schwarz inequality and Young inequality.The result iswidely used in physics and mechanics,and it plays a significant role in the research of differential equations.

关 键 词：微分算子 特征值 特征函数 上界 不等式 

分 类 号：O175.1[理学—数学]