一类高阶方程的非线性边界条件的奇摄动问题  

A class of singular perturbed problems with nonlinear boundary value conditions for higher order equations

作　　者：刘燕[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241000

出　　处：《高校应用数学学报（A辑）》2012年第2期175-181,共7页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(10901003);安徽高校省级自然科学基金(KJ2011A135)

摘　　要：研究了一类非线性高阶微分方程的奇摄动问题.运用合成展开法构造了问题的形式渐进解,并运用了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,最后给出了一个例子说明结果的意义.A class nonlinear boundary value problems with singular perturbation for higher order differential equations are studied. The formal asymptotic solutions are constructed by the composite expansion method, and by using the theory of differential inequalities, the existence of solutions for the original problems and the uniform validity of the formal asymptotic solutions are proved. Finally, an example is given to illustrate the significance of the results.

关 键 词：奇摄动 非线性 高阶微分方程 微分不等式理论 

分 类 号：O175.14[理学—数学]