奇摄动三阶非线性方程边值问题的套层解  

Jacketed solution of the boundary value problem of third order nonlinear differential equations

作　　者：陈秀[1] 

机构地区：[1]合肥学院数理系,安徽合肥230022

出　　处：《合肥工业大学学报（自然科学版）》2005年第12期1621-1623,共3页Journal of Hefei University of Technology：Natural Science

基　　金：安徽省教育厅自然科学基金资助项目(2003KJ287)

摘　　要：研究一类三阶非线性微分方程边值问题的奇摄动,由于退化问题是一阶微分方程,将失去两个初值条件,所以摄动解在x=0的某一邻域内将出现非一致性。文中揭示了其解呈现双重层性质,即奇摄动问题的解在该区域内呈现不同“厚度”的初始层性质;在适当的假设条件下,通过引进不同量级的伸长变量,构造不同“厚度”的初始层校正项,并利用微分不等式理论,得到了解的任意次近似的一致有效的渐近展开式。This paper deals with the singular perturbation of the boundary value problem of a class of third order nonlinear differential equations. It is shown that the solution has double layer behavior. By introducing extended variables and using the theory of differential inequality, the uniformly effective asymptotic expansion is obtained under appropriate conditions.

关 键 词：套层解 微分不等式 渐近展开 奇摄动三阶非线性方程 边值问题 

分 类 号：O175.8[理学—数学]