Abstract A special method is proposed for reducing an $$n $$ -dimensional system of second-order ordinary differential equations to a $$2n$$ -dimensional system of first-order ones. Using matrix weight functions (which can be chosen arbitrarily when applying the method), we establish sufficient conditions for the boundedness and power-law absolute integrability on the half-line of the components of all solutions to a linear system of second-order differential equations and their first derivatives as well as for their decay (in particular, exponential or power-law) as the independent variable tends to infinity. An illustrative example is provided.

中文翻译：

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研究半线上二阶线性微分方程组解的渐近性质的方法

摘要 提出一种将$$n$$维二阶常微分方程组化简为$$2n$$一阶常微分方程组的特殊方法。利用矩阵权函数（在应用该方法时可以任意选择），我们建立了一个二阶微分方程线性系统的所有解的分量的半线上的有界性和幂律绝对可积性的充分条件以及它们的一阶导数以及它们的衰减（特别是指数或幂律），因为自变量趋于无穷大。提供了一个说明性示例。