二阶拟线性常微分方程组边值问题的奇摄动Singular Perturbations of a Boundary Value Problem for a Second Order Quasi-Linear System of Differential Equations
林元刚;
摘要(Abstract):
本文研究二阶拟线性常微分方程组边值问题εy″+A(t,y,ε)y′十g(t,y,ε)=0y(0,ε)=α(ε),y(1,ε)=β(ε)其中ε>0是小参数,y,g,α,β是n维向量函数,A是n×n矩阵函数。假设退化问题A(t,y,0)y′+g(t,y,0)=0,y(1)=β(0)有解y_0(t),则加上一些其他条件后,便可推知当ε>0充分小时,存在摄动问题的解y(t,ε),它和它的导函数可表为y(t,ε)=sum from i=0 to m(y_i(t)εi十O(εi十O(ε(m+1))+O(e(m+1))+O(e(-μi/ε))y′(t,ε)=sum from i=0 to m(y_i′(t)ε(-μi/ε))y′(t,ε)=sum from i=0 to m(y_i′(t)εi十O(εi十O(ε(m+1))+O(ε(m+1))+O(ε(-1)e(-1)e(-μi/ε))其中y_1(t),…,y_m(t)可依次由具有递推形式的一阶常微分方程组的终值问题解出。
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基金项目(Foundation):
作者(Authors): 林元刚;
参考文献(References):
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