Numerical solution of the sturm liouville problem with periodic boundary conditions

1971 ◽  
pp. 277-289 ◽  
Author(s):  
D. J. Evans
Keyword(s):  
Boundary Conditions ◽  
Numerical Solution ◽  
Periodic Boundary ◽  
Liouville Problem ◽  
Periodic Boundary Conditions ◽  
Sturm Liouville

The inverse Sturm-Liouville problem with generalized periodic boundary conditions

2008 ◽  
Vol 78 (1) ◽  
pp. 582-584
Author(s):  
V. A. Sadovnichii ◽  
Ya. T. Sultanaev ◽  
A. M. Akhtyamov
Keyword(s):  
Boundary Conditions ◽  
Periodic Boundary ◽  
Liouville Problem ◽  
Periodic Boundary Conditions ◽  
Sturm Liouville

Inverse Sturm-Liouville problem with generalized periodic boundary conditions

2009 ◽  
Vol 45 (4) ◽  
pp. 526-538 ◽  
Author(s):  
V. A. Sadovnichii ◽  
Ya. T. Sultanaev ◽  
A. M. Akhtyamov
Keyword(s):  
Boundary Conditions ◽  
Periodic Boundary ◽  
Liouville Problem ◽  
Periodic Boundary Conditions ◽  
Sturm Liouville

scholarly journals A counterexample in Sturm–Liouville completeness theory

2004 ◽  
Vol 134 (2) ◽  
pp. 241-248 ◽  
Author(s):  
Paul Binding ◽  
Branko Ćurgus
Keyword(s):  
Boundary Conditions ◽  
Riesz Basis ◽  
Periodic Boundary ◽  
Dirichlet Boundary ◽  
Liouville Problem ◽  
Periodic Boundary Conditions ◽  
Dirichlet Boundary Conditions ◽  
Indefinite Weight ◽  
Sturm Liouville

We give an example of an indefinite weight Sturm-Liouville problem whose eigenfunctions form a Riesz basis under Dirichlet boundary conditions but not under anti-periodic boundary conditions.

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.

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