Criterion for the solvability of a class of nonlinear two-point boundary value problems on the plane

被引：1

作者：

Mukhamadiev, E. ^{[1
]}

Naimov, A. N. ^{[1
]}

机构：

[1] Vologda State Univ, Vologda, Russia

来源：

DIFFERENTIAL EQUATIONS | 2016年 / 52卷 / 03期

基金：

俄罗斯基础研究基金会;

关键词：

Unit Circle; Nonlinear Term; Homogeneous Mapping; Nonzero Solution; Continuous Bounded Mapping;

D O I：

10.1134/S0012266116030071

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the solvability of a class of nonlinear two-point boundary value problems for systems of ordinary second-order differential equations on the plane. In these boundary value problems, we single out the leading nonlinear terms, which are positively homogeneous mappings. On the basis of properties of the leading nonlinear terms, we prove a criterion for the solvability of boundary value problems under arbitrary perturbations in a given set by using methods for the computation of the winding number of vector fields.

引用

页码：327 / 334

页数：8

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