转移条件下边界中含有谱参数的两类三阶边值问题的研究  

Two classes of third order boundary value problems with spectral parameters in the boundary under transmission conditions

作　　者：朱军伟 顾丽娜 李生彪[2] ZHU Junwei;GU Lina;LI Shengbiao(Yangling Vocational&Technical College,Yangling 712100,China;Lanzhou University of Arts and Science,Lanzhou 730000,China)

机构地区：[1]杨凌职业技术学院,陕西杨凌712100 [2]兰州文理学院,兰州730000

出　　处：《延边大学学报（自然科学版）》2022年第4期303-311,共9页Journal of Yanbian University（Natural Science Edition）

基　　金：甘肃省教育科技创新项目(2022A-174);杨凌职业技术学院校内项目(GJ20-105)。

摘　　要：在转移条件下利用判断函数和Rouche定理研究了如下边界中含有谱参数的两类三阶边值问题:{(py″)′+qy=λwy,A_(λ)Y(a)+B_(λ)Y(b)=0,CY(c-)+DY(c+)=0;{(py′)″+qy=λwy,A_(λ)Y(a)+B_(λ)Y(b)=0,CY(c-)+DY(c+)=0.研究结果显示,该问题至多有m+n+2个特征值.该结果可为研究奇数阶微分方程边值问题的有限谱提供参考.Using the iterative construction of the characteristic function and Rouche’s theorem under transmission conditions,the following two classes of third order boundary value problems with spectral parameters are studied:{(py″)′+qy=λwy,A_(λ)Y(a)+B_(λ)Y(b)=0,CY(c-)+DY(c+)=0;{(py′)″+qy=λwy,A_(λ)Y(a)+B_(λ)Y(b)=0,CY(c-)+DY(c+)=0.The results of the study showed that problems had at most m+n+2 eigenvalues.The results can provide a reference for the finite spectrum of boundary value problems of odd order differential equations.

关 键 词：转移条件 谱参数 判断函数 ROUCHE定理 

分 类 号：O175.8[理学—数学]