一类具有转移条件的不连续微分算子的渐近状态(英文)  

Asymptotic Behavior of a Discontinuous Differential Operator with Transmission Conditions

作　　者：杨秋霞[1,2] 王万义[1] 

机构地区：[1]内蒙古大学数学科学学院,内蒙古呼和浩特010021 [2]德州学院计算机系,山东德州253023

出　　处：《应用数学》2011年第1期15-24,共10页Mathematica Applicata

基　　金：Supported by the National Nature Science Foundation of China (10661008);the Na-tional Nature Science Foundation of Nei mongo (200711020102)

摘　　要：研究一类具有转移条件且边界条件依赖于特征参数的Sturm-Liouville算子,建立一个与其相关的新的空间框架,给出其特征的相关性质与特征函数的完备性,利用函数论方法得出其特征的渐近表示,并获得Green函数的表达式.In this paper, a Sturm-Liouville operator with eigenparameter-dependent boundary conditions and transmission conditions is studied. A new self-adjoint operator A is defined in an appropriate space H such that the eigenvalues of such a problem coincide with those of A. Asymptotic approximation formulae of its eigenvalues and completeness of its eigenfunctions are discussed, then asymptotic formulae for Green function is obtained.

关 键 词：Sturm—Liouville算子 特征值 特征函数 GREEN函数 转移条件 

分 类 号：O175.3[理学—数学]