重正化群方法已成为获得这类问题精确解的一致有效渐近展开式的有用工具。

Renormalization group method is an effective tool to obtain the uniformly valid asymptotic expansion exact solutions of this kind of problems.

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在一般的条件下，证明了解的存在性，而且得到解及其各导数的高阶一致有效渐近展开式。

Under the general conditions, we prove the existence of the solution and get the asymptotic expansions of the solution and its derivatives, which are uniformly valid for the higher orders.

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我们利用边界层校正法以及微分不等式理论证明了解的存在定理，并构造出其解的一致有效渐近展开式。

Using the method of boundary layer correction and the differential inequality theory, we prove the existence theorem of solutions and construct the uniformly valid asymptotic expansions of.

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