摘要
今研究下述一阶非线性向量微分方程初值问题。εy′=f(t,y,ε) t∈(a,b) (1) y(α,ε)=A[ξ(ε),y(t,ε),ε]=g[ξ(ε),ε]+f_a^bF(s,y(s,ε),ε)ds (2)其中ε>0为小参数,y=(y_1,y_2,…y_n),g=(g_1,g_2,…,g_n),F=(F_1,F_2,…,F_n),f=(f_1,f_2,…,f_n)为n维向量函数。本文提供了构造上述奇摄动初值问题解的渐近展开式,并利用微分不等式法讨论解的估计。
In this paper, we consider a class of first order nonlinear vector differential equations with initial data: εy′= f(t, y, ε) t∈(a,b) (1) y(a,ε)= A[ζ(ε), y(t,ε), ε]=g[ζ(ε), ε]+integral from a=1 to b F(s, y(s, ε), ε)ds (2) here f, y, g, F, are the functions of n-dimensional vectors. By using the methods of boundary layer correction and differential inequalities, we obtain the asymptotic solution and estimation of the oriainal problem.
基金
国家自然科学基金资助项目
关键词
非线性
奇摄动
微分不等式
Nonlinear
Singular perturbation
Differential inequality.
