具有k个不连续点且边条件含有特征参数的四阶对称微分方程的自共轭性  

Self-Adjointness of Fourth-Order Symmetrical Differential Equation with k Discontinuous Points and Eigenparameter-Dependent Boundary Conditions

作　　者：王娟[1] 王桂霞[1] 刘知雨 

机构地区：[1]内蒙古师范大学数学科学学院

出　　处：《内蒙古师范大学学报（自然科学汉文版）》2014年第2期137-141,共5页Journal of Inner Mongolia Normal University(Natural Science Edition)

基　　金：教育部重点项目(212029);内蒙古自然基金资助项目(2013MS0116);内蒙古高等学校科学研究重点项目(NJZZ13037)

摘　　要：在研究单边带特征参数的不连续微分算子的基础上,研究了双边带特征参数且具有k个不连续点的四阶微分算子的自共轭性.构造了一个适当的Hilbert空间H,在新空间H中定义一个与问题相关的算子T,证明了算子T在H中不仅是对称的,而且是自共轭的.This paper is to investigate the self-adj ointness of fourth-order symmetrical differential equation with k discontinuous points and eigenparameter-dependent boundary conditions.It is based on discontinuous differential operator with eigenvalue parameter in one boundary condition.The self-adj oint-ness of problem is studied in an appropriate Hilbert space H with a new defined operator T related to the problem.We prove the operator T is not only symmetric but also self-adjoint.

关 键 词：转移条件 特征参数 自共轭性 微分算子 

分 类 号：O175.3[理学—数学]