边界条件含特征参数的奇异不连续Sturm-Liouville算子的渐近特征  

Asymptotic Behaviors of a Second Order Singular Discontinuous Differential Operator with Eigenparameter Dependent Boundary Conditions

作　　者：周立广[1] 王万义[1] 索建青[1] 

机构地区：[1]内蒙古大学数学科学学院,呼和浩特010021

出　　处：《数学的实践与认识》2012年第18期242-251,共10页Mathematics in Practice and Theory

基　　金：国家自然科学基金(10961019)

摘　　要：研究有限区间内一类边界条件含特征参数的不连续奇异Sturm-Liouville问题.利用函数论和算子理论的方法,证明该问题的自伴性,得到其特征值的相关性质,基本解及其特征值的渐近公式.In this paper Strum-Liouville problem with eigenparameter dependent boundary conditions and with transmission conditions at finite points of considered finite interval is obtained. We prove that it＇s self-adjoint in a adequate Hilbert Space differential operator generated by this Singular Sturm-Liouville problem. Then some properties of the eigenvalues and asymptotic formulas for fundamental solutions and eigenvalues of the considered problem be investigated with function theory and operator method.

关 键 词：Sturm—Liouville问题 转移条件 渐近公式 

分 类 号：O175.3[理学—数学]