摘要
研究了一类含双参数的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近解,并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.
A class of two-parameter and 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. 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.
出处
《应用数学与计算数学学报》
2014年第1期62-71,共10页
Communication on Applied Mathematics and Computation
基金
国家自然科学基金资助项目(10901003)
安徽高校省级自然科学基金资助项目(KJ2011A135)
关键词
奇摄动
双参数
高阶微分方程
微分不等式理论
singular perturbation
two-parameter
higher order differential equations
theory of differential inequalities
