scholarly journals Spectral properties of boundary-value-transmission problems with a constant retarded argument

2019 ◽  
Vol 43 (2) ◽  
pp. 612-619
Author(s):  
Erdoğan ŞEN
Keyword(s):  
Spectral Properties ◽  
Boundary Value ◽  
Retarded Argument ◽  
Value Transmission ◽  
Transmission Problems

scholarly journals OSCILLATION PROPERTIES FOR NON-CLASSICAL STURM-LIOUVILLE PROBLEMS WITH ADDITIONAL TRANSMISSION CONDITIONS

2021 ◽  
Vol 26 (3) ◽  
pp. 432-443
Author(s):  
Oktay Sh. Mukhtarov ◽  
Kadriye Aydemir
Keyword(s):  
Boundary Value ◽  
Main Difficulty ◽  
Distribution Of Zeros ◽  
Value Transmission ◽  
Transmission Problems ◽  
New Type ◽  
Sturm Liouville ◽  
Left And Right ◽  
New Criteria ◽  
Oscillation Properties

This work is aimed at studying some comparison and oscillation properties of boundary value problems (BVP’s) of a new type, which differ from classical problems in that they are defined on two disjoint intervals and include additional transfer conditions that describe the interaction between the left and right intervals. This type of problems we call boundary value-transmission problems (BVTP’s). The main difficulty arises when studying the distribution of zeros of eigenfunctions, since it is unclear how to apply the classical methods of Sturm’s theory to problems of this type. We established new criteria for comparison and oscillation properties and new approaches used to obtain these criteria. The obtained results extend and generalizes the Sturm’s classical theorems on comparison and oscillation.

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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