A regularized trace formula and oscillation of eigenfunctions of a Sturm-Liouville operator with retarded argument at 2 points of discontinuity

2017 ◽  
Vol 40 (18) ◽  
pp. 7051-7061 ◽  
Author(s):  
Erdoğan Şen
Keyword(s):  
Trace Formula ◽  
Liouville Operator ◽  
Retarded Argument ◽  
Regularized Trace ◽  
Sturm Liouville ◽  
Points Of Discontinuity

scholarly journals The formula for the regularized trace of the Sturm-Liouville operator with a logarithmic potential

2019 ◽  
Vol 50 (3) ◽  
pp. 269-280
Author(s):  
Khabir Kabirovich Ishkin ◽  
Leisan Gainullovna Valiullina
Keyword(s):  
Trace Formula ◽  
Liouville Operator ◽  
Logarithmic Potential ◽  
Regularized Trace ◽  
Sturm Liouville

We have obtained a regularized trace formula for the Sturm-Liouville operator on a semi-axis with a logarithmic potential.

scholarly journals The second regularized trace formula for the Sturm-Liouville operator

2019 ◽  
Vol 20 (1) ◽  
pp. 17
Author(s):  
F. Aydin Akgun ◽  
M. Bayramoglu ◽  
A. Bayramov
Keyword(s):  
Trace Formula ◽  
Liouville Operator ◽  
Regularized Trace ◽  
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.

scholarly journals Asymptotic Behaviour of Eigenvalues and Eigenfunctions of a Sturm-Liouville Problem with Retarded Argument

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Erdoğan Şen ◽  
Jong Jin Seo ◽  
Serkan Araci
Keyword(s):  
Boundary Value Problem ◽  
Liouville Operator ◽  
Liouville Problem ◽  
Asymptotic Formulas ◽  
Retarded Argument ◽  
Eigenvalues And Eigenfunctions ◽  
Transmission Coefficients ◽  
Discontinuous Boundary ◽  
Sturm Liouville ◽  
Special Case

In the present paper, a discontinuous boundary-value problem with retarded argument at the two points of discontinuities is investigated. We obtained asymptotic formulas for the eigenvalues and eigenfunctions. This is the first work containing two discontinuities points in the theory of differential equations with retarded argument. In that special case the transmission coefficients and retarded argument in the results obtained in this work coincide with corresponding results in the classical Sturm-Liouville operator.

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