一类双参数奇摄动方程混合三点边值问题

A Class of Mixed Three-point Boundary Value Problems with Two-parameter Singularly Perturbed Equation

讨论了一类具混合三点边值条件的三阶微分方程的双参数奇摄动问题.首先,利用奇摄动方法求出问题的外部解;然后,引入两个不同的伸展变量构造了问题在边界附近的边界层校正项,得到了所提问题的形式渐近解;最后,运用微分不等式理论证明了问题解的存在性及所得形式渐近解的一致有效性.

This paper discussed a class of singularly perturbed problems with two parameters for third-order differential equations with mixed three-point boundary value conditions.Firstly,the outer solution was constructed by means of the singular perturbation method.Then,two different stretching variables were introduced,the boundary layer correction of solution were obtained,and the asymptotic analytic expansion solution to the original problem was also given.Finally,According to the theory of differential inequalities,the existence of solutions and the uniform validity of the asymptotic solutions were proved.