Finite Rank Perturbations in Pontryagin Spaces and a Sturm–Liouville Problem with λ-rational Boundary Conditions

2018 ◽  
pp. 163-189
Author(s):  
Jussi Behrndt ◽  
Friedrich Philipp
Keyword(s):  
Boundary Conditions ◽  
Finite Rank ◽  
Liouville Problem ◽  
Pontryagin Spaces ◽  
Sturm Liouville

Sturm-Liouville Problem for Stationary Differential Operator with Nonlocal Two-Point Boundary Conditions

2006 ◽  
Vol 11 (1) ◽  
pp. 47-78 ◽  
Author(s):  
S. Pečiulytė ◽  
A. Štikonas
Keyword(s):  
Boundary Condition ◽  
Differential Operator ◽  
Boundary Conditions ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Liouville Problem ◽  
Complex Case ◽  
Qualitative Behavior ◽  
Point Boundary ◽  
Sturm Liouville

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.

Inverse Sturm–Liouville problem with spectral polynomials in nonsplitting boundary conditions

2017 ◽  
Vol 53 (1) ◽  
pp. 47-55
Author(s):  
V. A. Sadovnichii ◽  
Ya. T. Sultanaev ◽  
A. M. Akhtyamov
Keyword(s):  
Boundary Conditions ◽  
Liouville Problem ◽  
Sturm Liouville

scholarly journals A Singular Sturm-Liouville Problem with Limit Circle Endpoints and Eigenparameter Dependent Boundary Conditions

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Jinming Cai ◽  
Zhaowen Zheng
Keyword(s):  
Boundary Conditions ◽  
Liouville Problem ◽  
Fundamental Solutions ◽  
Asymptotic Formulas ◽  
Limit Circle ◽  
Operator Formulation ◽  
Sturm Liouville ◽  
Completeness Of Eigenfunctions

In this paper, we investigate a class of discontinuous singular Sturm-Liouville problems with limit circle endpoints and eigenparameter dependent boundary conditions. Operator formulation is constructed and asymptotic formulas for eigenvalues and fundamental solutions are given. Moreover, the completeness of eigenfunctions is discussed.

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