这样，轴对称正交异性圆环壳的齐次解第一次有了达到薄壳理论精度的完全的渐近展开。
Thus, the fully asymptotic expansion of the homogeneous solution within the accuracy of theory of thin shells is obtained.
运用分歧理论，隐函数定理，以及渐近展开的方法，获得了非平凡周期解的存在性。
The existence of co-exist periodic solution is investigated by using the bifurcation theory, the implicit function theorem and the method of asymptotic expansion.
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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