奇摄动线性非齐次微分方程Cauchy问题的一种研究方法
A Method of the Study of the Cauchy Problem for a Singularly Perturbed Linear Inhomogeneous Differential Equation
摘要：
构造了一个序列，它收敛于任意阶奇摄动线性非齐次微分方程柯西问题的解。这个序列也是一个渐近序列在以下意义上：偏差（在连续函数空间的范数）的$n$第th元素的解决方案的问题是成比例的$(n+1)$ th权力的参数扰动。这个序列可以用来证明由边界函数法得到的渐近性。
英文摘要：
We construct a sequence that converges to a solution of the Cauchy problem for a singularly perturbed linear inhomogeneous differential equation of an arbitrary order. This sequence is also an asymptotic sequence in the following sense: the deviation (in the norm of the space of continuous functions) of its $n$th element from the solution of the problem is proportional to the $(n+1)$th power of the parameter of perturbation. This sequence can be used for justification of asymptotics obtained by the method of boundary functions.
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