摘要
本文用微分不等式的方法和技巧,研究了一类高阶非线性系统两点边值问题: εy^(n)=f(t,y,y',…,y^((n-1)),ε),0<t<1, y^((j))(0,ε)=A_j(ε)(0≤j≤n-2),y^((n-2))(1,ε)=B(ε)。其中ε是正的小参数,y,A_j(0≤j≤n-2,n≥2),B,f是m维向量函数。在适当的假设条件下,根据其退化问题的解在(0,1)内是否具有连续的(n-1)阶导数,即出现边界层现象和角层现象时,证明了此边值问题当ε→0^+时其解的存在性和渐近性质。
In this paper, using the method and technique of differential inequalities, we study the exis-tence and asymptotic behavior , as ε→o+ , of the solutions of vector boundary value problemsTwo types of asymptotic behavior are studied depending on whether the reduced solution has a continuous (n- l)th- order derivative in (0,1) or not, leading to the phenomena of boundary and angular layers.
出处
《高校应用数学学报（A辑）》
CSCD
北大核心
1991年第1期100-109,共10页
Applied Mathematics A Journal of Chinese Universities(Ser.A)
基金
国家自然科学基金
