关键词: 空间对照结构, 渐近展开, 边界层函数法, 光滑缝接法, 奇异摄动理论

Abstract: We considered the boundary value problem of a class of piecewise-smooth singularly perturbed ordinary differential equation with critical case. Firstly, we constructed a asymptotical approximation of solution with internal and boundary layers by using the boundary function method and smooth matching method. Then we used the intermediate value theorem to prove the existence of solution of the problem, and gave the accuracy of the constructed asymptotical approximation.

Key words: spatial contrast structure, asymptotical approximation, boundary function method, smooth matching method, singular perturbation theory