On the General Nonlinear Self-Adjoint Eigenvalue Problem for Systems of Ordinary Differential Equations with Singularities

被引：1

作者：

Abramov, A. A. ^{[1
]}

Ul'yanova, V. I. ^{[1
]}

Yukhno, L. F. ^{[2
]}

机构：

[1] Russian Acad Sci, Dorodnicyn Comp Ctr, Moscow 119333, Russia

[2] Russian Acad Sci, Inst Math Modeling, Moscow 125047, Russia

来源：

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS | 2010年 / 50卷 / 01期

基金：

俄罗斯基础研究基金会;

关键词：

ordinary differential equation; nonlinear self-adjoint eigenvalue problem; eigenvalues; numerical method for determining the number of eigenvalues;

D O I：

10.1134/S0965542510010057

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A nonlinear self-adjoint eigenvalue problem for the general linear system of ordinary differential equations is examined on an unbounded interval. A method is proposed for the approximate reduction of this problem to the corresponding problem on a finite interval. Under the assumption that the initial data are monotone functions of the spectral parameter, a method is given for determining the number of eigenvalues lying on a prescribed interval of this parameter. No direct calculation of eigenvalues is required in this method.

引用

页码：32 / 37

页数：6

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