具有三个转向点的大参数奇摄动方程  

A Class of Singularly Perturbed Equations for Larger Parameter with Three Turning Points

作　　者：韩祥临[1] 李璜[2] 欧阳成[1] 

机构地区：[1]湖州师范学院理学院,湖州310013 [2]杭州电子科技大学理学院,杭州310018

出　　处：《应用数学学报》2014年第4期687-695,共9页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11071205);浙江省自然科学基金(LY13A010005,Y6110502)资助项目

摘　　要：讨论了一类具有三个转向点的大参数奇摄动方程.利用Liouville-Green变换和Airy函数,分别得到了方程的外部解和内层解;用匹配法给出了方程解在七个不同区域上的渐近表达式中七对常数所满足的六个匹配条件;并说明了对具有多个转向点的此类方程可作相应推广.Firstly,a class of large parameter singularly perturbed equations with three turning points is discussed.Using Liouville-Green transformation and Airy functions,the outer solution and the interior solution of the equation are obtained;using matching method,six matched conditions satisfied by seven pairs of constant among asymptotic expressions of the solution of the equation in seven different regions are given.Secondly,it is illustrated that for this class of equations with multi turning points the corresponding result can be generalized.

关 键 词：奇摄动 转向点 Liouville-Green变换 匹配法 AIRY函数 

分 类 号：O[理学]