一类奇摄动高阶方程非线性多点边值问题

A class of nonlinear multi-point boundary value problems of singularly perturbed higher order equations

讨论了一类具非线性多点边值条件的高阶方程的奇摄动问题,利用奇摄动方法,首先求出问题的外部解,再利用伸展变量,构造问题在边界处的边界层校正项,得到原问题的形式渐近解。最后,利用微分不等式理论证明解的存在性和一致有效性。

A class of singularly perturbed problems of higher order differential equations with nonlinear multi-point boundary value conditions were discussed.Firstly,the outer solution was constructed by means of the singular perturbation method.Then utilizing a stretched variable to construct the boundary layer correction of solution,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 are proved.