A New Method of Solving the Index Problem for Sturm-Liouville Eigenvalues  

作　　者：GUI-XIA WANG JIONG SUN 

机构地区：[1]College of Mathematics science,Inner Mongolia Normal University [2]Mathematics Department,Inner Mongolia University

出　　处：《Acta Mathematicae Applicatae Sinica》2015年第4期1001-1012,共12页应用数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China(No.11361039 and 11161030);the Natural Science Foundation of Inner Mongolia Province,China(No.2013MS0116)

摘　　要：Based on some recent results for interlacing eigenvalue intervals from 1-parameter families of se- quences of eigenvalue inequalities, a new method is given to solving the index problem for Sturm-Liouville eigenvalues for coupled self-adjoint boundary conditions in the regular case. The key is a new characteristic principle for indices for Sturm-Liouville eigenvalues. The algorithm corresponding on the characteristic princi- ple are discussed, and numerical examples are presented to illustrate the theoretical results and show that the algorithm is valid.Based on some recent results for interlacing eigenvalue intervals from 1-parameter families of se- quences of eigenvalue inequalities, a new method is given to solving the index problem for Sturm-Liouville eigenvalues for coupled self-adjoint boundary conditions in the regular case. The key is a new characteristic principle for indices for Sturm-Liouville eigenvalues. The algorithm corresponding on the characteristic princi- ple are discussed, and numerical examples are presented to illustrate the theoretical results and show that the algorithm is valid.

关 键 词：self-adjoint Sturm-Liouville problems indices of eigenvalues coupled boundary conditions Priiferangle Interlacing Eigenvalue Intervals numerical computations. 

分 类 号：O151.21[理学—数学] O241.6[理学—基础数学]