Finite Spectrum Of Boundary Value Problems For Differential Equations With Transmission Conditions And Spectral Parameters In The Boundary Conditions

In this thesis,we mainly study the finite spectrum of a class of boundary value problems for differential equations with transmission conditions and spectral parameters in the boundary conditions,by using the construction of the solution of the discontinuous function and the iteration of the characteristic function,and Rotuche's theorem.The paper is divided into three chapters:the content is the following:In chapter 1,we firstly introduce the historical background of boundary value prob-lems.Next,we briefly explain the finite spectrum of differential boundary value problems with transmission conditions and spectral parameters in the boundary conditions.Finally,we summary the contributions of scholars to the finite spectrtum of differential equation boundary value problems in recent years,and research problems of the thesis.In chapter 2,we research the finite spectrum of a class of Sturm-Liouville problems with n transmission conditions and spectral parameters in the boundary conditions.For any p ositive integer n and a set of positive integers mi,i=0,1,…,n,it has at most m0+m1+…+mn+2n+1 eigenvalues.In chapter 3,we investigate two classes of finite spectrum of third order boundary value problems with transmission conditions and spectral parameters in the boundary conditions.For any positive integer n,m,it is calculated that there are at most m+n+2 eigenvalues.