一类四阶微分方程的奇摄动边值问题  

A class of singularly perturbed boundary value problems for fourth order differential equations

作　　者：许友伟[1] 姚静荪[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：《高校应用数学学报（A辑）》2014年第2期180-184,共5页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(11201004);安徽高校省级自然科学基金(KJ2011A135)

摘　　要：运用合成展开法和微分不等式理论研究了一类四阶方程的奇摄动边值问题.先运用合成展开法,构造了问题的形式渐近解,再运用微分不等式理论证明了原问题解的存在性及所得形式渐近解的一致有效性.最后用一个例子来说明所得结果的意义.Using the method of composite expansion and the theory of differential inequality, a class of singularly perturbed boundary value problems for fourth order equations are studied. The formal asymptotic solutions of the problems are constructed by the method of composite expansion. Then the existence of solutions for the original problems and the uniform validity of the formal asymptotic solutions are proved by the theory of differential inequality. At last, an example is given to illustrate the significance of the obtained result.

关 键 词：奇摄动 边值问题 单边Nagumo条件 微分不等式理论 

分 类 号：O175.14[理学—数学]