一类2n阶具有转移条件的对称微分算子的特征值问题  

The Eigenvalue Problems for 2n-order Symmetric Differential Operators with Transmission Conditions

作　　者：陈文娟 孙炯[1] CHEN Wen-juan;SUN Jiong(School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China)

机构地区：[1]内蒙古大学数学科学学院

出　　处：《数学的实践与认识》2018年第11期200-205,共6页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11161030,11561150,11401325)

摘　　要：研究了具有边界条件及转移条件的2n阶对称微分算子的特征值问题．首先构建了新的Hilbert空间使得所研究的微分算子在新的Hilbert空间中是自共轭的．然后利用微分算子谱分析经典方法，得到了λ是边值问题的特征值的充要条件，并给出了边值问题特征值的某些特点．In this paper, we study the eigenvalue problems of the 2n-order symmetric differential operators with boundary and transmission conditions. First, we construct a new Hilbert Space, so that the investigated differential operators are self-adjoint. And then, by using the basic methods of spectral analysis, we obtain the sufficient and necessary conditions for λ to be the eigenvalue of the boundary value problems and some properties of the eigenvalues of the boundary value problems.

关 键 词：对称微分算子 转移条件 特征值 边值问题 

分 类 号：O175.3[理学—数学]