scholarly journals Variational principles for spectral analysis of one Sturm-Liouville problem with transmission conditions

2016 ◽  
Vol 2016 (1) ◽  
Author(s):  
Kadriye Aydemir ◽  
Oktay Sh Mukhtarov
2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nida Palamut Koşar

AbstractIn the present study, we investigate the existence of spectral functions and obtain the Parseval identity and expansion formula in eigenfunctions for the singular q-Sturm–Liouville problem with transmission conditions.


2002 ◽  
Vol 81 (6) ◽  
pp. 1283-1305 ◽  
Author(s):  
G. Freiling ◽  
V. Rykhlov ◽  
V. Yurko

2006 ◽  
Vol 11 (1) ◽  
pp. 47-78 ◽  
Author(s):  
S. Pečiulytė ◽  
A. Štikonas

The Sturm-Liouville problem with various types of two-point boundary conditions is considered in this paper. In the first part of the paper, we investigate the Sturm-Liouville problem in three cases of nonlocal two-point boundary conditions. We prove general properties of the eigenfunctions and eigenvalues for such a problem in the complex case. In the second part, we investigate the case of real eigenvalues. It is analyzed how the spectrum of these problems depends on the boundary condition parameters. Qualitative behavior of all eigenvalues subject to the nonlocal boundary condition parameters is described.


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