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

共 50 条

[21] Determination of the Number of an Eigenvalue of a Singular Nonlinear Self-Adjoint Spectral Problem for a Linear Hamiltonian System of Differential Equations
Abramov, A. A.
Ul'yanova, V. I.
Yukhno, L. F.
DIFFERENTIAL EQUATIONS, 2011, 47 (08) : 1110 - 1115
[22] Eigenvalue singular problem of factorized fourth-order self-adjoint differential equations
Caruntu, Dumitru I.
APPLIED MATHEMATICS AND COMPUTATION, 2013, 224 : 603 - 610
[23] On self-adjoint ordinary differential equations of the fourth order.
Whyburn, WM
AMERICAN JOURNAL OF MATHEMATICS, 1930, 52 : 171 - 196
[24] DEFICIENCY INDEX PROBLEM FOR ORDINARY SELF-ADJOINT DIFFERENTIAL OPERATORS
DEVINATZ, A
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1973, 79 (06) : 1109 - 1127
[25] SOLUTION BEHAVIOUR FOR GENERAL SELF-ADJOINT DIFFERENTIAL EQUATIONS
HUNT, RW
NAMBOODI.MS
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 1970, 21 (DEC) : 636 - &
[26] A 2-POINT BOUNDARY PROBLEM FOR ORDINARY SELF-ADJOINT DIFFERENTIAL EQUATIONS OF EVEN ORDER
KAUFMAN, H
STERNBERG, RL
DUKE MATHEMATICAL JOURNAL, 1953, 20 (04) : 527 - 531
[27] Linear ordinary self-adjoint differential equations of the second order.
Wheeler, AP
AMERICAN JOURNAL OF MATHEMATICS, 1927, 49 : 309 - 320
[28] DISCONJUGACY CRITERIA FOR SYSTEMS OF SELF-ADJOINT DIFFERENTIAL EQUATIONS
SIMONS, W
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1973, 6 (FEB): : 373 - 381
[29] On certain properties of a nonlinear eigenvalue problem for Hamiltonian systems of ordinary differential equations
Abramov A.A.
Ui'yanova V.I.
Yukhno L.F.
Computational Mathematics and Mathematical Physics, 2007, 47 (4) : 612 - 619
[30] Self-adjoint commuting ordinary differential operators
Andrey E. Mironov
Inventiones mathematicae, 2014, 197 : 417 - 431

← 1 2 3 4 5 →