Abstract

The nonlinear two-point boundary value problem with parameter for systems of ordinary differential equations is investigated by the parametrization method. The method consists in partition of the interval apart, the introduction of additional parameters and reducing the original problem to the equivalent multi-point boundary value problem with parameters. The algorithms for finding a solution to the equivalent boundary value problem are constructed. The conditions for convergence of the algorithms that ensure the solvability of nonlinear two-point boundary value problem with parameter are obtained. Definition of the isolated solution to nonlinear two-point boundary value problem with parameter, which is a modification of the well-known definition for the nonlinear two-point boundary value problem without parameter, is introduced.

中文翻译：

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带有参数的非线性两点边值问题的孤立解的存在性

摘要

用参数化方法研究了常微分方程系统的带参数的非线性两点边值问题。该方法包括划分间隔，引入附加参数以及将原始问题简化为带参数的等效多点边界值问题。构造用于寻找等效边界值问题的解的算法。获得了确保具有参数的非线性两点边值问题的可解性的算法的收敛条件。介绍了带参数的非线性两点边值问题的孤立解的定义，它是对无参数的非线性两点边值问题的著名定义的修改。