二阶非线性微分方程非线性三点边值问题的奇摄动  

Singular perturbation of nonlinear three-point boundary value problem for second order nonlinear differential equations

作　　者：许国安[1] 余赞平[2] 

机构地区：[1]华侨大学数学科学学院,福建泉州362021 [2]福建师范大学数学与计算机科学学院,福建福州350007

出　　处：《高校应用数学学报（A辑）》2013年第3期321-328,共8页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：华侨大学科研基金(10HZR25);中央高校基本科研业务费专项资金

摘　　要：研究二阶非线性微分方程非线性三点边值问题,利用微分不等式理论及"打靶法",证明了解的存在性,并在此基础上讨论奇摄动二阶非线性三点边值问题,构造了其高阶渐近解及得到解的一致有效估计.A class of nonlinear three-point boundary value problems for second order nonlinear differential equations are studied.By the theory of differential inequalities and the method of ＂shooting target＂,the existence of solution for original problems is proved.Furthermore,singular perturbed nonlinear boundary value problem for second order nonlinear differential equation is studied,the high order asymptotic solutions is constructed,and the error estimate of asymptotic solution and exact solution is obtained.

关 键 词：二阶非线性微分方程 非线性三点边值问题 奇摄动 存在性 

分 类 号：O175.14[理学—数学]