一类三阶非线性方程组边值问题的奇摄动

摘要

This paper presents singular perturbation of boundary value problems for a class of third order nonlinear vector systems. The existence and local uniqueness of Solutions, Constructions of asymptotic Solutions and their uniform validity of the problem are studied in the paper. Boundary functions are successfully constructed through finding out invariant manifolds at both end boundary layers and giving out decoupling conditions of boundary value conditions. As an application, a corresponding problem of an equation is discussed.%作者研究了一类三阶奇摄动非线性方程组边值问题解的存在唯一性及渐近解的构造和一致有效性。通过找出两端边界层的不变流形，并且给出边值条件解耦的条件，成功构造了边界层函数。作为应用，最后讨论了相应的方程式问题。