scholarly journals Spectral Problem for the Sturm–Liouville Operator with Retarded Argument Containing a Spectral Parameter in the Boundary Condition

2017 ◽  
Vol 68 (8) ◽  
pp. 1263-1277
Author(s):  
E. Şen ◽  
M. Acikgoz ◽  
S. Araci
Keyword(s):  
Boundary Condition ◽  
Spectral Problem ◽  
Spectral Parameter ◽  
Liouville Operator ◽  
Retarded Argument ◽  
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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