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山东大学学报（理学版） 산동대학학보（이학판）
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
2014年 4期 79-83 ,共5页

杨雪洁%孙国正%陈雯楊雪潔%孫國正%陳雯

양설길%손국정%진문

奇摄动%内层%合成展开法%不动点定理奇攝動%內層%閤成展開法%不動點定理
기섭동%내층%합성전개법%불동점정리
singular perturbation%interior layer%the method of composite expansion%fixed point theorem

研究了一个具有内层现象的奇摄动微分方程边值问题，利用合成展开法和分析技巧构造了该问题的零阶近似解，并利用不动点定理证明了解的存在性，给出了精确解和渐近解的误差估计。
연구료일개구유내층현상적기섭동미분방정변치문제，이용합성전개법화분석기교구조료해문제적령계근사해，병이용불동점정리증명료해적존재성，급출료정학해화점근해적오차고계。
A singularly perturbed differential equation boundary value problem with interior layer phenomenon is studied. The zero order approximate solution of this problem is constructed using the method of composite expansions and analyt-ical skills.According to the fixed point theorem, the existence of solution is proved and the error estimate of asymptotic solution is given.