On discontinuous Dirac systems with eigenvalue dependent boundary conditions

2015 ◽  
Author(s):  
Etibar S. Panakhov ◽  
Tuba Gulsen
Keyword(s):  
Boundary Conditions ◽  
Dirac Systems ◽  
Eigenvalue Dependent Boundary Conditions

Sturm–Liouville problems with non-separated eigenvalue dependent boundary conditions

2000 ◽  
Vol 130 (2) ◽  
pp. 239-247 ◽  
Author(s):  
P. A. Binding ◽  
P. J. Browne
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Separated Boundary Conditions ◽  
Sturm Liouville ◽  
Eigenvalue Dependent Boundary Conditions

Sturm–Liouville differential equations are studied under non-separated boundary conditions whose coefficients are first degree polynomials in the eigenparameter. Situations are examined where there are at most finitely many non-real eigenvalues and also where there are only finitely many real ones.

Darboux transformations and the factorization of generalized Sturm–Liouville problems

2010 ◽  
Vol 140 (1) ◽  
pp. 1-29 ◽  
Author(s):  
Paul A. Binding ◽  
Patrick J. Browne ◽  
Bruce A. Watson
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Darboux Transformation ◽  
Darboux Transformations ◽  
Sturm Liouville ◽  
Eigenvalue Dependent Boundary Conditions

A version of the Darboux transformation is explored for Sturm-Liouville problems with eigenvalue-dependent boundary conditions, from differential-equation and operator-theoretic viewpoints. Some of the literature on Darboux's transformation is related in a historical introduction.

scholarly journals Principal Functions of Non-Selfadjoint Sturm-Liouville Problems with Eigenvalue-Dependent Boundary Conditions

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Nihal Yokuş
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Differential Expression ◽  
Spectral Singularities ◽  
Sturm Liouville ◽  
Eigenvalue Dependent Boundary Conditions ◽  
Complex Valued

We consider the operator generated in by the differential expression , and the boundary condition , where is a complex-valued function and , with . In this paper we obtain the properties of the principal functions corresponding to the spectral singularities of .

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