一个奇摄动四阶微分方程的非线性混合边值问题  

A nonlinear mixed boundary value problem for singularly perturbed forth-order differential equation

作　　者：陈雯[1] 姚静荪[1] 杨雪洁[1] 

机构地区：[1]安徽师范大学数学计算机科学学院,安徽芜湖241003

出　　处：《山东大学学报（理学版）》2015年第3期67-72,共6页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11271020)

摘　　要：研究了一个带非线性混合边界条件的四阶非线性微分方程的奇摄动边值问题。运用合成展开法构造了该问题的形式渐近解,并利用微分不等式理论证明了该问题解的存在性,给出了渐近解关于精确解的误差估计。A singularly perturbed boundary value problem for forth-order nonlinear differential equation with nonlinear mixed boundary condition is studied. The formal asymptotic solution is constructed by using the composite expansion method. According to the theory of differential inequalities,the existence of solution for the problem is proved and the error estimate of asymptotic solution is given.

关 键 词：奇摄动 四阶微分方程 合成展开法 微分不等式理论 

分 类 号：O175.14[理学—数学]