In this study, impulsive singular dynamic Dirac equations are considered.
Firstly, a spectral function for these equations is constructed. Later, an
integral representation of the resolvent operator is obtained

Allahverdiev, Bilender P.

Isayev, Hamlet A.

Tuna, Hüseyin

Khazar University Institutional Repository

Analele Universităţii OradeaFasc. Matematica, Tom XXXI (2024), Issue No. 1, 115–126THE RESOLVENT OPERATOR OF SINGULAR IMPULSIVEDYNAMIC DIRAC EQUATIONSBILENDER P. ALLAHVERDIEV1, HÜSEYIN TUNA2 AND HAMLET A. ISAYEV3Abstract. In this study, impulsive singular dynamic Dirac equations are con-sidered. Firstly, a spectral function for these equations is constructed. Later, anintegral representation of the resolvent operator is obtained.References[1] B. P. Allahverdiev and H. Tuna, On the resolvent operator of dynamic Dirac operators, Adv.Math. Sci. Appl., 32 (1) (2023), 1-16.[2] B. P. Allahverdiev and H. Tuna, Impulsive Dirac system on time scales, Ukrainian Math. J.,75 (6) (2023), 723-735.[3] B. P. Allahverdiev and H. Tuna, Titchmarsh–Weyl theory for impulsive dynamic Dirac system,Qual. Theory Dyn. Syst. 22, 148 (2023), 1-10.[4] R. Kh. Amirov, On a system of Dirac differential equations with discontinuity conditions insidean interval, Ukrainian Math. J., 57 (5) (2005), 712-727.[5] K. Aydemir, H. Olğar and O. Sh. Mukhtarov, The principal eigenvalue and the principal eigen-function of a boundary-value-transmission problem, Turkish J. Math. Comput. Sci., 11 (2)(2019), 97-100.[6] K. Aydemir, H. Olgar, O. Sh. Mukhtarov and F. Muhtarov, Differential operator equationswith interface conditions in modified direct sum spaces, Filomat, 32 (3) (2018), 921-931.[7] M. Bohner and A. Peterson, Dynamic equations on time scales, Birkhäuser, Boston, 2001.[8] Ş. Faydaoğlu and G. Sh. Guseinov, Eigenfunction expansion for a Sturm–Liouville boundaryvalue problem with impulse, Int. J. Pure Appl. Math. 8 (2) (2003), 137-170.[9] Y. Güldü, On discontinuous Dirac operator with eigenparameter dependent boundary and twotransmission conditions, Bound. Value Probl. (2016), Paper No. 135.[10] D. Karahan and Kh. R. Mamedov, On a q-boundary value problem with discontinuity condi-tions, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 13 (4) (2021), 5-12.[11] D. Karahan and Kh. R. Mamedov, On a q-analogue of the Sturm–Liouville operator withdiscontinuity conditions, Vestn. Samar. Gos. Tekh. Univ., Ser. Fiz.-Mat. Nauk., 26 (3) (2022),407-418.[12] B. Keskin and A. S. Ozkan, Inverse spectral problems for Dirac operator with eigenvalue de-pendent boundary and jump conditions, Acta Math. Hungarica, 130 (2011), 309-320.[13] H. Koyunbakan and E. S. Panakhov, Solution of a discontinuous inverse nodal problem on afinite interval, Math. Comput. Model., 44 (1-2) (2006), 204-209.[14] B. M. Levitan and I. S. Sargsjan, Sturm–Liouville and Dirac Operators, Mathematics and itsApplications (Soviet Series). Kluwer Academic Publishers Group, Dordrecht, 1991.[15] O. Sh. Mukhtarov, Discontinuous boundary-value problem with spectral parameter in boundaryconditions, Turkish J. Math., 18 (1994), 183-192.2020 Mathematics Subject Classification. 34N05, 34L40, 34A36, 47A10.Key words and phrases. Dynamic equations on time scales, Dirac operator, discontinuous equa-tions, resolvent.115116 BILENDER P. ALLAHVERDIEV, HÜSEYIN TUNA AND HAMLET A. ISAYEV[16] A. Zettl, Adjoint and self-adjoint boundary value problems with interface conditions, SIAM J.Appl. Math. 16 (4) (1968), 851-859.Received 11 November 20231 Department of Mathematics, Khazar University, AZ1096 Baku, Azerbaijanand Research Center of Econophysics, UNEC-Azerbaijan State University of Econom-ics, Baku, Azerbaijan.2 Department of Mathematics, Mehmet Akif Ersoy University, 15030 Burdur, Turkey.3 Department of Mathematics, Khazar University, AZ1096 Baku, Azerbaijan.Email address: 1 bilenderpasaoglu@gmail.com, 2 hustuna@gmail.com, 3 hamlet@khazar.org

The Resolvent Operator of Singular Impulsive Dynamic Dirac Equations

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The Resolvent Operator of Singular Impulsive Dynamic Dirac Equations

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