摘要
本文应用高阶微分不等式技巧和边界层校正法研究一类高阶非线性方程混合边值问题: e^2y^(n)=f(t,e,y,…,y^(n-2) Pj(ε)y^(j)(0,ε)-qj(ε)y^(j+1)(0,ε)=Aj(ε) (0≤j≤n-3) a_d(ε)y(n-2)(0,ε)-a_2(ε)y^(n-1)(0,ε)=B(ε) b_1(ε)y(n-2)(1,ε)十b_2(ε)y(n-1)(1,ε)=C(ε)的奇异摄动。在较一般的条件下,证明了摄动解的存在性,并得到了摄动解直到n阶导函数的一致有效渐近展开式,从而推广和改进了前人的结果。
In this paper, it has been studied that the singular perturbations for the higher order nonlinear boundary value problem of the form
by the method of higher order differential inequalities and boundary layer corrections. Under some mild conditions, the existence of the perturbed solution is proved and its uniformly efficient asymptotic expansions up to its nth-order derivative function are given out. Hence, the existing results are extended and improved.
出处
《应用数学和力学》
EI
CSCD
北大核心
1996年第12期1129-1136,共8页
Applied Mathematics and Mechanics
关键词
非线性
边值问题
奇摄动
微分不等式
摄动解
nonlinear boundary value problem, singular perturbation, uniformly efficient asymptotic expansion, higher order differential inequalities, boundary layer correction
