scholarly journals Asymptotics for eigenvalues of Sturm - Liouville operator with periodic boundary conditions

2014 ◽  
Vol 6 (3) ◽  
pp. 28-34
Author(s):  
Alina Vyacheslavovna Karpikova
Keyword(s):  
Boundary Conditions ◽  
Liouville Operator ◽  
Periodic Boundary ◽  
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

scholarly journals On the Riesz Basisness of Systems Composed of Root Functions of Periodic Boundary Value Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Alp Arslan Kıraç
Keyword(s):  
Boundary Conditions ◽  
Riesz Basis ◽  
Liouville Operator ◽  
Periodic Boundary ◽  
Fourier Coefficients ◽  
Sufficient Conditions ◽  
Root Functions ◽  
Periodic Boundary Value Problems ◽  
Sturm Liouville ◽  
Necessary And Sufficient

We consider the nonself-adjoint Sturm-Liouville operator withq∈L1[0,1]and either periodic or antiperiodic boundary conditions. We obtain necessary and sufficient conditions for systems of root functions of these operators to be a Riesz basis inL2[0,1]in terms of the Fourier coefficients ofq.

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.

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