含两参数的三阶拟线性常微分方程边值问题的奇摄动

Singular Perturbation of Boundary Value Problem for Quasilinear Third Order Ordinary Differential Equations Involving Two Small Parameters

研究含两参数的三阶拟线性常微分方程奇摄动边值问题· 采用两阶段展开的方法 ,对ε/μ2 → 0 ( μ → 0 ) ;μ2 /ε→ 0 (ε→ 0 )和ε=μ2 三种情形构造出形式渐近解 ,同时利用微分不等式方法 ,证明了解的存在性 ,并给出余项的一致有效的估计·

The singularly perturbed boundary value problem for quasilinear third order ordinary differential equation involving two small parameters has been considered. For the three cases ε/μ 2→0(μ→0),μ 2/ε→0(ε→0) and ε=μ 2,the formal asymptotic solutions are constructed by the method of two steps expansions and the existences of solution are proved by using the differential inequality method. In addition, the uniformly valid estimations of the remainder term are given as well.