摘要
本文利用微分不等式理论研究了非线性微分方程组初边值问题:εy′=f(t,y,ε),0<t<1,y(0,ε)=A(ε)或y(1,ε)=B(ε)或y_i(0,ε)=A_i(ε),y_j(1,ε)=B_j(ε),i=1,2,…,k;j=k+1,…,n的奇摄动,其中ε>0为小参数,y、f、A和B为n推向量函数。在适当的条件下证明了解的存在,求得解及其任意阶的一致有效渐近展开式,并对余项做出了估计。
In this paper, using the theory of differential inequality, we consider the singular perturbation of initial and boundary value problem for systems, of nonlinear differential equation: ey'= f(t,y,ε), 0,<t<1, y(0,ε) = A(ε), or y(1,ε) =B(e),. or y_1(0,ε)=A_1 (ε), y_1(1,ε), = B_j(ε), y_j(1,ε)= 1, 2, … ,k; j=k+ 1,… , n,,Where ε<0 is a small parameter, y, f, A and B are n-dimensional functions. Under appropriate assumptions the existence of solution and its uniformly valid asymptotic expansion of arbitrary order are proved, and estimation corresponding to the remainder term is given.
出处
《福建师范大学学报（自然科学版）》
CAS
CSCD
1990年第3期23-28,共6页
Journal of Fujian Normal University：Natural Science Edition
基金
国家自然科学基金
关键词
非线性系统
边值
奇摄动
初边值
nonlinear system, initial and boundary value problem, singular perturbation, asymptotic expansion
