The Finite Spectrum of Sturm–Liouville Problems with Transmission Conditions and Eigenparameter-Dependent Boundary Conditions

2012 ◽  
Vol 63 (3-4) ◽  
pp. 1057-1070 ◽  
Author(s):  
Ji-jun Ao ◽  
Jiong Sun ◽  
Mao-zhu Zhang
Keyword(s):  
Boundary Conditions ◽  
Transmission Conditions ◽  
Finite Spectrum ◽  
Sturm Liouville

scholarly journals Discontinuous Sturm-Liouville Problems and Associated Sampling Theories

2011 ◽  
Vol 2011 ◽  
pp. 1-30 ◽  
Author(s):  
M. M. Tharwat
Keyword(s):  
Boundary Conditions ◽  
Green’S Function ◽  
Green's Function ◽  
Eigenfunction Expansion ◽  
Green’S Functions ◽  
Transmission Conditions ◽  
Expansion Theorem ◽  
Sampling Theorems ◽  
Sturm Liouville ◽  
Special Case

This paper investigates the sampling analysis associated with discontinuous Sturm-Liouville problems with eigenvalue parameters in two boundary conditions and with transmission conditions at the point of discontinuity. We closely follow the analysis derived by Fulton (1977) to establish the needed relations for the derivations of the sampling theorems including the construction of Green's function as well as the eigenfunction expansion theorem. We derive sampling representations for transforms whose kernels are either solutions or Green's functions. In the special case, when our problem is continuous, the obtained results coincide with the corresponding results in the work of Annaby and Tharwat (2006).

scholarly journals The Finite Spectrum of Fourth-Order Boundary Value Problems with Transmission Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Fang-zhen Bo ◽  
Ji-jun Ao
Keyword(s):  
Boundary Conditions ◽  
Finite Number ◽  
Boundary Value Problems ◽  
Fourth Order ◽  
Boundary Value ◽  
Transmission Conditions ◽  
Finite Spectrum ◽  
Fourth Order Problems

A class of fourth-order boundary value problems with transmission conditions are investigated. By constructing we prove that these class of fourth order problems consist of finite number of eigenvalues. Further, we show that the number of eigenvalues depend on the order of the equation, partition of the domain interval, and the boundary conditions (including the transmission conditions) given.

scholarly journals Finite spectrum of Sturm-Liouville problems with eigenparameter-dependent boundary conditions on time scales

Filomat ◽  
2019 ◽  
Vol 33 (6) ◽  
pp. 1747-1757
Author(s):  
Ji-Jun Ao ◽  
Juan Wang
Keyword(s):  
Spectral Analysis ◽  
Boundary Conditions ◽  
Time Scales ◽  
Liouville Equation ◽  
Time Scale ◽  
The Self ◽  
Finite Spectrum ◽  
Sturm Liouville

The spectral analysis of a class of Sturm-Liouville problems with eigenparameter-dependent boundary conditions on bounded time scales is investigated. By partitioning the bounded time scale such that the coefficients of Sturm-Liouville equation satisfy certain conditions on the adjacent subintervals, the finite eigenvalue results are obtained. The results show that the number of eigenvalues not only depend on the partition of the bounded time scale, but also depend on the eigenparameter-dependent boundary conditions. Both of the self-adjoint and non-self-adjoint cases are considered in this paper.

Sign in / Sign up

Export Citation Format

Share Document