【摘要】 研究了一类具有边界层性质的奇摄动拟线性边值问题。在相对较弱的条件下,利用合成展开法构造问题的形式近似解,然后利用不动点定理证明解的存在性,并给出满足边界层性质的高阶近似解,使得它与精确解之间的渐近估计可达到任意O(ε~n)阶近似。更多还原

【Abstract】 Some singularly perturbed quasilinear boundary value problems with boundary layer properties are studied.Under the weaker conditions,the formal approximation of the problem is constructed using the method of composite expansions.The existence of solutions are proved and a higher order approximate solution of the problem is gained by the fixed point theorem.It is shown that an asymptotic estimation of any order O(ε~n) approximation is achieved between the exact solution and approximate solution.Key word:更多还原