一类具有n阶转向点的大参数奇摄动方程的特征值问题  

A Class of Singularly Perturbed Eigenvalue Problem for Large Parameter with Turning Point of n-th Order

作　　者：史娟荣[1,2] 

机构地区：[1]安徽师范大学数学与计算机学院,安徽芜湖241003 [2]安徽机电职业技术学院,安徽芜湖241002

出　　处：《安徽工业大学学报（自然科学版）》2015年第3期289-292,共4页Journal of Anhui University of Technology（Natural Science）

基　　金：国家自然科学基金项目(11202106);安徽高校自然科学重点研究项目(KJ2015A418);国内访问学者项目经费资助

摘　　要：讨论一类具有n阶转向点的大参数奇摄动方程的特征值问题。首先,利用一个特殊的变换将原具有n阶转向点的大参数问题转化为便于讨论的问题;其次,求得了用特殊函数表示的渐近解,并研究所得到解的性态,指出了该解为具有n阶转向点的大参数奇摄动问题渐近解的一致有效性;再次,利用所给的边界条件求出了原问题的特征函数和特征值;最后,用定理形式论述相应的大参数问题的结果,并指出当n=1时与前人讨论的结果一致。A class of possessing n-th order turning point eigenvalue problem of singular perturbation equation for large parameter is discussed. Firstly, substituting the original possessing n-th order turning point problem for large parameter is turned into studied problem; Secondly, the asymptotic solution using the characteristic function representation is obtained; Then the behavior of the received solution is studied, and this asymptotic solution of possessing n-th order turning point eigenvalue problem for large parameter is uniformly valid; And then, the characteristic functions and characteristic values for the original problem are solved by using the boundary conditions;Finally, the conclusion of corresponding large parameter problem is discussed using the theorem, and it is pointed out that it is the same with that of previous study when n is equal to one.

关 键 词：转向点 Langer变换 AIRY函数 特征值 

分 类 号：O175.14[理学—数学]