一类非线性向量微分方程无穷边值问题的奇摄动  

The Singular Perturbation of Boundary Value Problem on Infinite Interval for a Class Nonlinear Vector Differential Equation

作　　者：林苏榕[1] 

机构地区：[1]福建广播电视大学计算机系,福州350003

出　　处：《数学物理学报（A辑）》2014年第3期727-737,共11页Acta Mathematica Scientia

基　　金：福建省教育厅科技项目(JA11288)资助

摘　　要：讨论一类非线性向量微分方程无穷边值问题的奇摄动,虽然此类边值问题在有限区间上曾被广泛地研究过,但在无限区间上还未曾采用对角化的方法去研究它.在适当的条件下,该文采用新的方法去证明解的存在性和任意阶的一致有效的渐近展开式,同时也给出误差估计.The paper discuss the singular perturbation of boundary value problem on infinite interval for a class nonlinear vector differential equation.Although,the boundary problem on the finite interval had been treated extensiverly,but on the infinite interval it has not been studied using the diagonalization method.Under appropriate assumptions,we use new method to prove the existence of solution and the uniformly valid asymptotice expansion of arbitrary order and the error estimation are given as well.

关 键 词：无穷区间 边值问题 奇异摄动 对角化方法 

分 类 号：O175[理学—数学]