具有积分边界条件的二阶奇摄动问题的内层

摘要

研究一类具有积分边界条件的二阶奇摄动问题的内层.假设退化方程解在定义区间上某点不光滑,运用边界层函数法和缝接法,构造出形式渐近解,然后利用上下解定理证明这类问题解的存在性,同时给出精确解的估计.最后利用数值例子说明该方法的有效性.%The existence and asymptotic estimates of solutions for a class of singularly perturbed boundary value with the internal layer problem is investigated.Assume that the solution of the degenerate equation is not smooth at the defined interval,by using the boundary function method and the sewing method,the formal asymptotic solution is constructed.Then the exist-ence of the solution are proved by using the theorem of lower-upper solutions,and an exact so-lution is estimated.Finally,an numerical example is presented as an illustration.