一类边界条件带有谱参数且具有转移条件的四阶微分算子(英文)  

A Class of Fourth-order Differential Operator With Eigenparameter-dependent Boundary and Transmission Conditions

作　　者：张新艳[1,2] 孙炯[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]内蒙古财经大学统计与数学学院,内蒙古呼和浩特010070

出　　处：《应用数学》2013年第1期205-219,共15页Mathematica Applicata

基　　金：Supported by the National Nature Science Foundation of China (10861008,11161030)

摘　　要：本文研究一类在内部不连续点具有转移条件且特征参数不仅出现在微分方程中而且出现在四个边界条件中的四阶正则微分算子.通过构造与问题相关的新线性算子A,证明在适当的希尔伯特空间H中算子A是自共轭的当且仅当条件CTQ1C=ρQ1,θ2ATQ2A=θ1BTQ2B=θ1θ2Q1,θ2AQ1AT=θ1BQ1BT=θ1θ2Q2成立.利用微分方程的基本解证明λ是问题的特征值当且仅当det(Aλ+BλΦ(1,λ))=0.最后得到算子A仅有点谱.We investigate a class of fourth-order regular differential operator with transmission con- ditions at an interior discontinuous point when an eigenparameter appears not only in the differential equation but also appears in four boundary conditions. By constructing a new linear operatorA asso- ciated with the problem,we prove that the operator A is self-adjoint in a suitable Hilbert space H, if and only if the conditions CtQ1C = pQ1,θ2ATQ2A = θ1BTQ2B = θ1 θ2 Q1 ,θ2 AQ1AT = θ1BQ1BT = θ1 θ2 Q2 hold. And in term of basic solutions of differential equation, we show that the A is an eigen- value of the problem if and only if det（Aλ -b Bλφ（1 ,λ）） = O. We get that the operator A has only point spectrum.

关 键 词：四阶微分算子 自共轭性 含特征参数边界条件 转移条件 特征值 点谱 

分 类 号：O175.3[理学—数学]