高阶转向点问题  

Problems on the High-order Turning Point

作　　者：周钦德[1] 邓寿安 李勇[1] 

机构地区：[1]吉林大学数学系

出　　处：《吉林大学自然科学学报》1989年第1期23-32,共10页Acta Scientiarum Naturalium Universitatis Jilinensis

基　　金：国家自然科学基金

摘　　要：证明了小参数问题εy″+f(x,ε)y′+g(x,ε)y=0,y(-a)=a(ε),y(b)=β(ε)解的存在唯一性和一致有效渐近展开,其中ε>0,f(0,0)=,f′(0,0)=…=f^(m-1)(0,0)=0,f^(m)(0,0)≠0,m是一大于2的奇数。The existence, uniqueness, and asymptotic expansion of the solution to the boundary value problem with a small parameter ε〉0 εy'+ f(X,ε)y'+g(x,ε)y=0 y(-a)=a(ε), y(b)=β(ε) are given, where f(0,0)=f'(0,0)=…=f^(m-1)(0,0)=0, f^(m)(0,0)≠0, m is an odd number. The results previously obtained by many authors are concerned With the case m=l, but the case we consider here is that m≥2, in such a situation this problem becomes more complicated.

关 键 词：奇异摄动 转向点 边值问题 

分 类 号：O241.81[理学—计算数学]