A trace formula for the Sturm-Liouville type equation with retarded argument

Hıra, Fatma

doi:10.1501/commua1_0000000782

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

2017

DOI: 10.1501/commua1_0000000782

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A trace formula for the Sturm-Liouville type equation with retarded argument

Fatma Hıra¹

Abstract: Abstract. In this paper, we deal with a discontinuous Sturm-Liouville problem with retarded argument and eigenparameter-dependent boundary conditions. We obtain the asymptotic formulas for the eigenvalues and the regularized trace formula for the problem.

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Cited by 5 publications

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

Şen

2017

Math Methods in App Sciences

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Communicated by: P. M. Mariano MOS Classification: 34B24; 47A10; 47A55In this study, first, a formula for regularized sums of eigenvalues of a Sturm-Liouville problem with retarded argument at 2 points of discontinuity which contains a spectral parameter in the boundary conditions is obtained. After that, oscillation properties of the related problem is investigated. Finally, under the condition that a subset of nodal points is dense in definition set, the potential function is determined.

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

Şen

2017

Math Methods in App Sciences

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Spectrum, trace and nodal points of a Sturm–Liouville type delayed differential operator with interface conditions

Şen¹

2021

Rocky Mountain J. Math.

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Computation of Trace and Nodal Points of Eigenfunctions for a Sturm-Liouville Problem with Retarded Argument

Şen

2018

Cumhuriyet Science Journal

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In this study, a formula for regularized sums of eigenvalues and nodal points of eigenfunctions for a discontinuous Sturm-Liouville problem with a constant retarded argument. Contrary to standart problems the spectral parameter appears not only in the differential equation, but also in one of the boundary conditions. Thus, we see whether the nodal points of eigenfunctions and the trace change or not.

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A trace formula for the Sturm-Liouville type equation with retarded argument

Abstract: Abstract. In this paper, we deal with a discontinuous Sturm-Liouville problem with retarded argument and eigenparameter-dependent boundary conditions. We obtain the asymptotic formulas for the eigenvalues and the regularized trace formula for the problem.

Cited by 5 publications

References 20 publications

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

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

Spectrum, trace and nodal points of a Sturm–Liouville type delayed differential operator with interface conditions

Computation of Trace and Nodal Points of Eigenfunctions for a Sturm-Liouville Problem with Retarded Argument

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