带变号权函数的分数阶Laplace算子的特征值问题

发布时间：2018-06-20 19:51

本文选题：分数阶Laplace + 特征值　；参考：《兰州大学》2017年硕士论文

【摘要】：微分算子是线性算子中最基本的一类无界算子,在数学物理以及其他学科中都有广泛的作用.线性微分算子的特征值和特征函数是算子理论的核心之一,也是研究相应的非线性问题的基础.本文讨论了有界区域上权函数变号的分数阶Laplace算子特征值问题(?)特征值和特征函数的性质.得到上述问题一列特征值序列的存在,尤其证明了第一特征值λ1,是简单的.紧接着在对权函数g(x)为有界可测的假设下,讨论了特征值所对应的正的特征函数的存在性,所得到的结论缩小了非负特征函数对应的特征值的范围,这些结果推广了Yang等人[Int. J. Bifur. Chaos. 2015],Servadei 等人[Discrete Contin. Dyn. Syst. 2013]及 Brown等人[J. Math. Anal.Appl. 1980]的主要结果.
[Abstract]:Differential operators are the most basic class of unbounded operators in linear operators, which play a wide role in mathematics, physics and other disciplines. The eigenvalues and eigenfunctions of linear differential operators are the core of operator theory and the basis of studying the corresponding nonlinear problems. In this paper, we discuss the eigenvalue problem of fractional Laplace operator on bounded domain. The properties of eigenvalues and eigenfunctions. The existence of a sequence of eigenvalues is obtained, especially the first eigenvalue 位 1 is proved to be simple. Then the existence of positive eigenfunctions corresponding to eigenvalues is discussed under the assumption that the weight function gx is bounded and measurable. The results obtained reduce the range of eigenvalues corresponding to non-negative eigenfunctions. These results generalize Yang et al. [Int.] J. Bifur. Chaos. 2015. Dyn. Syst. Brown et al. [J. Math. Anal.Appl. 1980.
【学位授予单位】：兰州大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175.3

【参考文献】