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中文摘要：
利用重正规化理论讨论了一类2阶2n＋1次非线性奇摄动微分方程,得到解的一致有效表达式.所得结果当n=1时即是相关文献中分别用格林函数方法和逐步近似解法得出的结果.同时将方程推广到更一般的形式,得到所讨论方程小振幅解的表达式,揭示了该方程还具有其它性态的解,且丰富推广了一些相应结论.为讨论相关类型的非线性方程提供了一种简捷有效的方法.
英文摘要：
Using renormalization theory,a class of second-order 2 n ＋ 1times nonlinear singular perturbation differential equation is studied and the expression is gotten.As n = 1,this is consistent with the result that is gotten using Green＇s Function and step approximation solution in the literature.At the same time,extending the equation to general,the expression of the solution with small amplitude is obtained.Then it is revealed that there are other behavior solutions for the equation.The correspondent results are popularized.A simple effective method is provided for discussion related types of nonlinear equations.
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