The uniformly valid asymptotic solution to the original initial boundary value problems was obtained by the theory of differential inequalities.
利用微分不等式理论，得到了原初始边值问题解的一致有效的渐近解。
The uniformly valid asymptotic expansion of solution for the problem is obtained.
得到了问题解的一致有效的渐近展开式。
Using the fixed point principle and the theory of differential inequality, we prove the existence of the solution and an uniformly valid asymptotic expansions of the solution is given as well.
利用不动点原理及微分不等式理论，我们证明了边值问题解的存在性，并给出了解的一致有效渐近展开式。
And then, the uniform validity of solution is proved and the uniform valid asymptotic expansions of arbitrary order are obtained by using the theories of differential inequalities.
然后，运用微分不等式理论，证明了形式渐近解的一致有效性，并得出了解得任意阶的一致有效展开式。
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.
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.
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。
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