A non-standard multiparameter eigenvalue problem in ordinary differential equations

被引：2

作者：

Faierman, M

Mennicken, R ^{[1
]}

机构：

[1] Univ Regensburg, Math NWF 1, D-93053 Regensburg, Germany

[2] Univ New S Wales, Sch Math, Sydney, NSW 2052, Australia

来源：

MATHEMATISCHE NACHRICHTEN | 2005年 / 278卷 / 12-13期

关键词：

multiparameter; eigenvalues; eigenfunction expansion;

D O I：

10.1002/mana.200410321

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider two simultaneous Sturm-Liouville systems involving three spectral parameters. However unlike the standard multiparameter problem, we now suppose that the principal part of each of the differential operators involved is multiplied by a different parameter. For such a non-standard system we establish the oscillation theory and discuss the associated eigenfunction expansion. Some open problems concerning the eigenfunction expansion are also presented. (c) 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

引用

页码：1550 / 1560

页数：11

共 50 条

[1] LEFT DEFINITE MULTIPARAMETER EIGENVALUE PROBLEM IN ORDINARY DIFFERENTIAL EQUATIONS
KALLSTROM, A
SLEEMAN, BD
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1976, 74 : 145 - 155
[2] Non-standard oscillation theory for multiparameter eigenvalue problems
Binding, P. A.
Volkmer, H.
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2012, 142 (04) : 673 - 690
[3] NON-STANDARD ANALYSIS AND SINGULAR PERTURBATIONS OF ORDINARY DIFFERENTIAL-EQUATIONS
ZVONKIN, AK
SHUBIN, MA
RUSSIAN MATHEMATICAL SURVEYS, 1984, 39 (02) : 69 - 131
[4] SINGULAR PERTURBATIONS OF ORDINARY DIFFERENTIAL-EQUATIONS AND NON-STANDARD ANALYSIS
CARTIER, P
ASTERISQUE, 1982, (92-9) : 21 - 44
[5] Modification of a method for solving the multiparameter eigenvalue problem for systems of loosely coupled ordinary differential equations
E. D. Kalinin
Computational Mathematics and Mathematical Physics, 2013, 53 : 874 - 881
[6] Modification of a method for solving the multiparameter eigenvalue problem for systems of loosely coupled ordinary differential equations
Kalinin, E. D.
COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2013, 53 (07) : 874 - 881
[7] ORDINARY DIFFERENTIAL-EQUATIONS AND THE SYMMETRIC EIGENVALUE PROBLEM
DEIFT, P
NANDA, T
TOMEI, C
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1983, 20 (01) : 1 - 22
[8] Overview of differential equations with non-standard growth
Harjulehto, Petteri
Hasto, Peter
Le, Ut V.
Nuortio, Matti
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 72 (12) : 4551 - 4574
[9] Perturbation Formulas for a Nonlinear Eigenvalue Problem for Ordinary Differential Equations
A. A. Abramov
L. F. Yukhno
Computational Mathematics and Mathematical Physics, 2018, 58 : 858 - 862
[10] ON AN EIGENVALUE PROBLEM OF AHMAD AND LAZER FOR ORDINARY DIFFERENTIAL-EQUATIONS
GAUDENZI, M
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1987, 99 (02) : 237 - 243

← 1 2 3 4 5 →