Azad Bayramov - Academia.edu (original) (raw)
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Papers by Azad Bayramov
In this work we obtain the regularized trace formula for an evenorder differential operator with ... more In this work we obtain the regularized trace formula for an evenorder differential operator with unbounded operator coefficient.
Hacettepe Journal of Mathematics and Statistics, 2019
The spectral problem\[-y''+q(x)y=\lambda y,\ \ \ \ 0<x<1\]\[y(0)=0, \quad y'(0)... more The spectral problem\[-y''+q(x)y=\lambda y,\ \ \ \ 0<x<1\]\[y(0)=0, \quad y'(0)=\lambda(ay(1)+by'(1)),\]is considered, where lambda\lambdalambda is a spectral parameter, q(x)inL1(0,1)q(x)\in{{L}_{1}}(0,1)q(x)inL1(0,1) is a complex-valued function, aaa and bbb are arbitrary complex numbers which satisfy the condition ∣a∣+∣b∣ne0|a|+|b|\ne 0∣a∣+∣b∣ne0. We study the spectral properties (existence of eigenvalues, asymptotic formulae for eigenvalues and eigenfunctions, minimality and basicity of the system of eigenfunctions in Lp(0,1){{L}_{p}}(0,1)Lp(0,1)) of the above-mentioned Sturm-Liouville problem.
Journal of Inequalities and Applications, 2011
In this study, a discontinuous boundary-value problem with retarded argument which contains a spe... more In this study, a discontinuous boundary-value problem with retarded argument which contains a spectral parameter in the boundary condition and with transmission conditions at the point of discontinuity is investigated. We obtained asymptotic formulas for the eigenvalues and eigenfunctions. MSC (2010): 34L20; 35R10.
In this work a Sturm-Liouville type problem with retarded argument which contains spectral parame... more In this work a Sturm-Liouville type problem with retarded argument which contains spectral parameter in the boundary conditions and with transmission conditions at the point of discontinuity are investigated. We obtained asymptotic formulas for the eigenvalues and eigenfunctions.
In this work a Sturm-Liouville type problem with retarded argument which contains spectral parame... more In this work a Sturm-Liouville type problem with retarded argument which contains spectral parameter in the boundary conditions and with transmission conditions at the point of discontinuity are investigated. We obtained asymptotic formulas for the eigenvalues and eigenfunctions.
Mathematical Methods in the Applied Sciences, 2012
In this paper, we have obtained the second regularized trace formula for the differential operato... more In this paper, we have obtained the second regularized trace formula for the differential operator equation with the semi-periodic boundary conditions.
In this work we obtain the regularized trace formula for an evenorder differential operator with ... more In this work we obtain the regularized trace formula for an evenorder differential operator with unbounded operator coefficient.
Hacettepe Journal of Mathematics and Statistics, 2019
The spectral problem\[-y''+q(x)y=\lambda y,\ \ \ \ 0<x<1\]\[y(0)=0, \quad y'(0)... more The spectral problem\[-y''+q(x)y=\lambda y,\ \ \ \ 0<x<1\]\[y(0)=0, \quad y'(0)=\lambda(ay(1)+by'(1)),\]is considered, where lambda\lambdalambda is a spectral parameter, q(x)inL1(0,1)q(x)\in{{L}_{1}}(0,1)q(x)inL1(0,1) is a complex-valued function, aaa and bbb are arbitrary complex numbers which satisfy the condition ∣a∣+∣b∣ne0|a|+|b|\ne 0∣a∣+∣b∣ne0. We study the spectral properties (existence of eigenvalues, asymptotic formulae for eigenvalues and eigenfunctions, minimality and basicity of the system of eigenfunctions in Lp(0,1){{L}_{p}}(0,1)Lp(0,1)) of the above-mentioned Sturm-Liouville problem.
Journal of Inequalities and Applications, 2011
In this study, a discontinuous boundary-value problem with retarded argument which contains a spe... more In this study, a discontinuous boundary-value problem with retarded argument which contains a spectral parameter in the boundary condition and with transmission conditions at the point of discontinuity is investigated. We obtained asymptotic formulas for the eigenvalues and eigenfunctions. MSC (2010): 34L20; 35R10.
In this work a Sturm-Liouville type problem with retarded argument which contains spectral parame... more In this work a Sturm-Liouville type problem with retarded argument which contains spectral parameter in the boundary conditions and with transmission conditions at the point of discontinuity are investigated. We obtained asymptotic formulas for the eigenvalues and eigenfunctions.
In this work a Sturm-Liouville type problem with retarded argument which contains spectral parame... more In this work a Sturm-Liouville type problem with retarded argument which contains spectral parameter in the boundary conditions and with transmission conditions at the point of discontinuity are investigated. We obtained asymptotic formulas for the eigenvalues and eigenfunctions.
Mathematical Methods in the Applied Sciences, 2012
In this paper, we have obtained the second regularized trace formula for the differential operato... more In this paper, we have obtained the second regularized trace formula for the differential operator equation with the semi-periodic boundary conditions.