scholarly journals On calculation of eigenvalues and eigenfunctions of a Sturm-Liouville type problem with retarded argument which contains a spectral parameter in the boundary condition

2011 ◽  
Vol 2011 (1) ◽  
Author(s):  
Erdoğan Şen ◽  
Azad Bayramov
Keyword(s):  
Boundary Condition ◽  
Spectral Parameter ◽  
Retarded Argument ◽  
Type Problem ◽  
Liouville Type ◽  
Eigenvalues And Eigenfunctions ◽  
Sturm Liouville

scholarly journals Transmission problem for the Sturm-Liouville equation involving a retarded argument

Filomat ◽  
2021 ◽  
Vol 35 (6) ◽  
pp. 2071-2080
Author(s):  
Erdoğan Şen
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Spectral Parameter ◽  
Liouville Equation ◽  
Spectral Properties ◽  
Asymptotic Formulas ◽  
Retarded Argument ◽  
Eigenvalues And Eigenfunctions ◽  
Discontinuous Boundary ◽  
Sturm Liouville

In this work, spectral properties of a discontinuous boundary-value problem with retarded argument which contains a spectral parameter in the boundary conditions and in the transmission conditions at the point of discontinuity are investigated. To this aim, asymptotic formulas for the eigenvalues and eigenfunctions are obtained.

On a Discontinuous Sturm—Liouville Type Problem with Retarded Argument

2011 ◽  
Author(s):  
Erdoğan Şen ◽  
Azad Bayramov ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras ◽  
...  
Keyword(s):  
Retarded Argument ◽  
Type Problem ◽  
Liouville Type ◽  
Sturm Liouville

Bounds for distance between eigenvalues of boundary value problems with retarded argument

2019 ◽  
Vol 69 (2) ◽  
pp. 399-408
Author(s):  
Erdoğan Şen
Keyword(s):  
Boundary Condition ◽  
Weight Function ◽  
Boundary Value Problems ◽  
Liouville Operator ◽  
Boundary Value ◽  
Physical Parameters ◽  
Retarded Argument ◽  
Transmission Coefficients ◽  
Sturm Liouville ◽  
Special Case

Abstract In this study we are concerned with spectrum of boundary value problems with retarded argument with discontinuous weight function, two supplementary transmission conditions at the point of discontinuity, spectral and physical parameters in the boundary condition and we obtain bounds for the distance between eigenvalues. We extend and generalize some approaches and results of the classical regular and discontinuous Sturm-Liouville problems. In the special case that ω (x) ≡ 1, the transmission coefficients γ1 = δ1, γ2 = δ2 and retarded argument Δ ≡ 0 in the results obtained in this work coincide with corresponding results in the classical Sturm-Liouville operator.

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