Limit theorems for one-dimensional boundary-value problems

被引：18

作者：

Kodlyuk, T. I. ^{[1
]}

Mikhailets, V. A. ^{[1
]}

Reva, N. V. ^{[2
]}

机构：

[1] Natl Acad Sci Ukraine, Inst Math, Kiev, Ukraine

[2] Ukrainian Natl Tech Univ, Kyiv Polytech Inst, Kiev, Ukraine

来源：

UKRAINIAN MATHEMATICAL JOURNAL | 2013年 / 65卷 / 01期

关键词：

SYSTEMS;

D O I：

10.1007/s11253-013-0766-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the limit with respect to a parameter in the uniform norm for the solutions of general boundary-value problems for systems of linear ordinary differential equations of the first order. A generalization of the Kiguradze theorem (1987) to this class of problems is obtained. The conditions imposed on the asymptotic behavior of the coefficients of systems are weakened as much as possible. Sufficient conditions for the uniform convergence of Green matrices to the Green matrix of the limit boundary-value problem are also established.

引用

页码：77 / 90

页数：14

共 20 条

[1]

[Anonymous], 1967, Lectures on the mathematical theory of stability

[2]

[Anonymous], DOP AKAD NAUK UKR RS

[3]

[Anonymous], 1962, UKR MAT ZH, DOI DOI 10.1007/BF02526637

[4]

Bogolyubov N. N., 1955, Asymptotic Methods in the Theory of Nonlinear Oscillations