非线性特征值的Brauer-型定位集  

Brauer-type localization of nonlinear eigenvalues

作　　者：李荣 李朝迁[1] LI Rong;LI Chaoqian(College of Mathematics and Statistics,Yunnan University,Kunming 650504,China)

机构地区：[1]云南大学数学与统计学院,云南昆明650504

出　　处：《纯粹数学与应用数学》2023年第1期1-10,共10页Pure and Applied Mathematics

基　　金：国家自然科学基金(12061087);云南省万人计划青年拔尖人才项目(YNWR-QNBJ-2018-095).

摘　　要：非线性特征值问题在阻尼结构动力分析,时滞系统稳定性分析,量子点的数值模拟和流固结构振动分析等领域有广泛应用,其特征值对于实际问题的解决至关重要.本文研究非线性特征值的定位问题,通过两行元素和加权技术得到了Brauer-型定位集及其简化形式,证明了其优于已有的结果,并应用其分析一类时滞系统的稳定性.Nonlinear eigenvalue problem is widely used in dynamic analysis of damped structures,stability analysis of time-delay systems,numerical simulation of quantum dots,vibration analysis of fluid-solid structures and many other fields,and its eigenvalues play an important role in practical applications.Brauer-type localization sets and their simplified forms are obtained by using the two-row elements and weighting methods,which are proved to be superior to the existing results,and are applied to analyze the stability of a class of time-delay systems.

关 键 词：非线性特征值 Brauer-型定位集 代数加权 几何加权 

分 类 号：O151.21[理学—数学]