一类奇摄动三阶非线性微分方程的两点边值问题

A Class Two Point Boundary Value Problem with Singular Perturbation for Third-order Nonlinear Differential Equation

本文研究如下一类带有小参数的三阶非线性微分方程两点边值问题{εym=f(t,y,y′,y′′ε),a<t<b y(a)=A(ε) y′′(a)=C(ε)y(b)B(ε)的解的高阶渐近展开,并利用压缩映像原理,证明了解的存在性并得到了解的高阶误差估计.

This paper studies the higher-order expansion of the solution of a class of two point boundary value problems for third-order nonlinear differential equation with small parameter as following{εym=f（t,y,y′,y′′ε）,atb y（a）=A（ε） y′′（a）=C（ε）y（b）B（ε） Then using Banach contraction mapping principle,proves the existence of solution and obtains the error estimate of the solution.