Small Solutions of Nonlinear Differential Equations Near Branching Points

被引：6

作者：

Sidorov, N. A. ^{[1
,2
]}

Sidorov, D. N. ^{[3
]}

机构：

[1] Irkutsk State Univ, Ul K Marksa 1, Irkutsk 664003, Russia

[2] Inst Syst Dynam & Control Theory, Irkutsk 664033, Russia

[3] Russian Acad Sci, Siberian Branch, Inst Energy Syst, Irkutsk 664033, Russia

来源：

RUSSIAN MATHEMATICS | 2011年 / 55卷 / 05期

基金：

俄罗斯基础研究基金会;

关键词：

Newton diagram; Jordan forms; Euler operator; branching; contracted mapping;

D O I：

10.3103/S1066369X11050070

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We construct parametric families of small branching solutions to nonlinear differential equations of the nth order near branching points. We use methods of the analytical theory of branching solutions of nonlinear equations and the theory of differential equations with a regular singular point. We illustrate the general existence theorems with an example of a nonlinear differential equation in a certain magnetic insulation problem.

引用

页码：43 / 50

页数：8

共 50 条

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