三阶非线性向量微分方程奇摄动边值问题解的高阶近似

Solution with Higher Order Approximations of the Singular Perturbation for Third-order Nonlinear Vector Differential Equations Boundary Value Problems

研究三阶非线性向量微分方程奇摄动边值问题,在适当的条件下,利用边界层校正法和对角化技巧,证得解的存在性并给出解的任意阶的一致有效的渐近展开式.

The singular perturbation of boundary value problem to a class of third-order nonlin- ear vector differential equations is studied. Under appropriate conditions, by using the boundary lay- er correction and diagonalization method, prove the existence of the solution of singular perturbation problem and obtain the uniformly valid asymptotic estimation with arbitrary order.