系数无界的线性微分方程组的有界解

IF 0.7 Q2 MATHEMATICS
R.Ye. Uteshova, Ye.V. Kokotova
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引用次数: 0

摘要

研究有限区间上具有无界系数矩阵的非齐次线性微分方程组的有界解问题。方程的右侧属于一个连续函数的空间,该空间有一定的权限;权重函数的选择要考虑系数矩阵的性质。采用非均匀划分参数化方法的改进版本对问题进行了研究。利用特殊结构的双侧无限矩阵,得到了问题适定性的充分必要条件。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On bounded solutions of linear systems of differential equations with unbounded coefficients
This paper deals with a problem of finding a bounded solution of a system of nonhomogeneous linear differential equations with an unbounded matrix of coefficients on a finite interval. The right-hand side of the equation belongs to a space of continuous functions bounded with some weight; the weight function is chosen taking into account the behavior of the coefficient matrix. The problem is studied using a modified version of the parameterization method with non-uniform partitioning. Necessary and sufficient conditions of well-posedness of the problem are obtained in terms of a bilaterally infinite matrix of special structure.
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来源期刊
CiteScore
1.20
自引率
50.00%
发文量
50
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