Spectrum and symmetries of the impulsive difference equations

Elgiz Bayram; Şerifenur Cebesoy; Seyda Solmaz

doi:10.31801/cfsuasmas.669708

Research Article

Year 2021, Volume: 70 Issue: 1, 38 - 51, 30.06.2021

Elgiz Bayram Şerifenur Cebesoy Seyda Solmaz

https://doi.org/10.31801/cfsuasmas.669708

Abstract

References

Samoilenko, A. M., Perestyuk, N. A., Impulsive differential equations, World Scientific, Singapore, 1995. Samoilenko, A. M., Perestyuk, N. A., Stability of the solutions of differential equations with impulsive action, Differencial'nye Uravnenija, 13(11) (1977), 1981-1992.
Perestyuk, N. A., Plotnikov, V. A., Samoilenko, A. M., Skripnik, N. V., Differential equations with impulse effects: multivalued right-hand sides with discontinuities, De Gruyter studies in mathematics 40, Germany, 2011.
Lakshmikantham, V., Bainov, D. D., Simeonov, P. S., Theory of impulsive differential equations, World Scientific, Singapore, 1998.
Bainov, D. D., Simeonov, P. S., Oscillation theory of impulsive differential equations, Int. Publ., Orlando, 1998.
He, Z. M., Zhang, X. M. , Monoton iterative technique for first order impulsive difference equations with periodic boundary conditions, Appl. Math. Comput., 156 (3) (2004), 605-620.
Wang, P., Wang, W., Boundary value problems for first order impulsive difference equations, Int. Journal of Difference Equations, 1 (2006), 249-259.
Zhang, Q., Q. , On a linear delay difference equations with impulses., Annals of Differential Equations, 18 (2), 197--204, (2002).
Krall, A.M., Bairamov, E., Cakar, O., Spectral analysis of a non-selfadjoint discrete Schrödinger operators with spectral singularities, Math. Nachr., 231 (2001), 89-104.
Bairamov, E., Cakar, O., Krall, A.M., Non-Selfadjoint Difference Operators and Jacobi Matrices with Spectral Singularities, Math. Nachr., 229 (2001), 5-14.
Adıvar, M., Bairamov, E., Difference Equations of Second Order with Spectral Singularities, J. Math. Anal. Appl., 277 (2003), 714--721.
Olgun, M., Koprubasi, T.,Aygar, Y., Principal Functions of Non-Selfadjoint Difference Operator with Spectral Parameter in Boundary Conditions, Abst. and Appl. Anal., 608329, (2011), 10 pp.
Naimark, M.A., Investigation of the spectrum and the expansion in eigenfunctions of a non-selfadjoit operators of second order on a semi-axis, AMS Transl., 2(16) (1960), 103-193.
Guseinov, G. Sh., On the concept of spectral singularities, Pramana J. Phys., 73(3) (2009), 587-603.
Bender, C. M., Boettcher, S., Real spectra in non-Hermitian Hamiltonians having PT symmetry, Phys. Rev. Lett., 80(24), (1998), 5243-5246.
Albeverio, S., Dabrowski, L., Kurasov, P., Symmetries of Schrödinger operators with Point Interactions, Letters in Mathematical Physics, 45 (1998), 33-47.
Mostafazadeh, A., Spectral Singularities of a General Point Interaction, J. Phys. A. Math. Theory, 44 (375302) (2011), 9 p).
Atkinson, F. V., Discrete and Continuous Boundary Problems, Academic Press Inc., 1964.

Spectrum and symmetries of the impulsive difference equations

Year 2021, Volume: 70 Issue: 1, 38 - 51, 30.06.2021

Elgiz Bayram Şerifenur Cebesoy Seyda Solmaz

https://doi.org/10.31801/cfsuasmas.669708

Abstract

This paper deals with the spectral analysis and symmetries of the second
order difference equations with impulse. We determine a transfer matrix and
this allows us to investigate the locations of eigenvalues and spectral
singularites of the difference operator generated in $\ell_{2}(\Z)$.

Keywords

Impulsive equations, eigenvalues, spectral singularities, symmetries

References

Samoilenko, A. M., Perestyuk, N. A., Impulsive differential equations, World Scientific, Singapore, 1995. Samoilenko, A. M., Perestyuk, N. A., Stability of the solutions of differential equations with impulsive action, Differencial'nye Uravnenija, 13(11) (1977), 1981-1992.
Perestyuk, N. A., Plotnikov, V. A., Samoilenko, A. M., Skripnik, N. V., Differential equations with impulse effects: multivalued right-hand sides with discontinuities, De Gruyter studies in mathematics 40, Germany, 2011.
Lakshmikantham, V., Bainov, D. D., Simeonov, P. S., Theory of impulsive differential equations, World Scientific, Singapore, 1998.
Bainov, D. D., Simeonov, P. S., Oscillation theory of impulsive differential equations, Int. Publ., Orlando, 1998.
He, Z. M., Zhang, X. M. , Monoton iterative technique for first order impulsive difference equations with periodic boundary conditions, Appl. Math. Comput., 156 (3) (2004), 605-620.
Wang, P., Wang, W., Boundary value problems for first order impulsive difference equations, Int. Journal of Difference Equations, 1 (2006), 249-259.
Zhang, Q., Q. , On a linear delay difference equations with impulses., Annals of Differential Equations, 18 (2), 197--204, (2002).
Krall, A.M., Bairamov, E., Cakar, O., Spectral analysis of a non-selfadjoint discrete Schrödinger operators with spectral singularities, Math. Nachr., 231 (2001), 89-104.
Bairamov, E., Cakar, O., Krall, A.M., Non-Selfadjoint Difference Operators and Jacobi Matrices with Spectral Singularities, Math. Nachr., 229 (2001), 5-14.
Adıvar, M., Bairamov, E., Difference Equations of Second Order with Spectral Singularities, J. Math. Anal. Appl., 277 (2003), 714--721.
Olgun, M., Koprubasi, T.,Aygar, Y., Principal Functions of Non-Selfadjoint Difference Operator with Spectral Parameter in Boundary Conditions, Abst. and Appl. Anal., 608329, (2011), 10 pp.
Naimark, M.A., Investigation of the spectrum and the expansion in eigenfunctions of a non-selfadjoit operators of second order on a semi-axis, AMS Transl., 2(16) (1960), 103-193.
Guseinov, G. Sh., On the concept of spectral singularities, Pramana J. Phys., 73(3) (2009), 587-603.
Bender, C. M., Boettcher, S., Real spectra in non-Hermitian Hamiltonians having PT symmetry, Phys. Rev. Lett., 80(24), (1998), 5243-5246.
Albeverio, S., Dabrowski, L., Kurasov, P., Symmetries of Schrödinger operators with Point Interactions, Letters in Mathematical Physics, 45 (1998), 33-47.
Mostafazadeh, A., Spectral Singularities of a General Point Interaction, J. Phys. A. Math. Theory, 44 (375302) (2011), 9 p).
Atkinson, F. V., Discrete and Continuous Boundary Problems, Academic Press Inc., 1964.

There are 17 citations in total.

Details

Primary Language	English
Subjects	Mathematical Sciences
Journal Section	Research Articles
Authors	Elgiz Bayram 0000-0003-2075-5016 Şerifenur Cebesoy 0000-0003-3571-6386 Seyda Solmaz 0000-0001-7572-2655
Publication Date	June 30, 2021
Submission Date	January 3, 2020
Acceptance Date	August 15, 2020
Published in Issue	Year 2021 Volume: 70 Issue: 1

Cite

APA	Bayram, E., Cebesoy, Ş., & Solmaz, S. (2021). Spectrum and symmetries of the impulsive difference equations. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 70(1), 38-51. https://doi.org/10.31801/cfsuasmas.669708
AMA	Bayram E, Cebesoy Ş, Solmaz S. Spectrum and symmetries of the impulsive difference equations. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. June 2021;70(1):38-51. doi:10.31801/cfsuasmas.669708
Chicago	Bayram, Elgiz, Şerifenur Cebesoy, and Seyda Solmaz. “Spectrum and Symmetries of the Impulsive Difference Equations”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70, no. 1 (June 2021): 38-51. https://doi.org/10.31801/cfsuasmas.669708.
EndNote	Bayram E, Cebesoy Ş, Solmaz S (June 1, 2021) Spectrum and symmetries of the impulsive difference equations. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70 1 38–51.
IEEE	E. Bayram, Ş. Cebesoy, and S. Solmaz, “Spectrum and symmetries of the impulsive difference equations”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 70, no. 1, pp. 38–51, 2021, doi: 10.31801/cfsuasmas.669708.
ISNAD	Bayram, Elgiz et al. “Spectrum and Symmetries of the Impulsive Difference Equations”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70/1 (June 2021), 38-51. https://doi.org/10.31801/cfsuasmas.669708.
JAMA	Bayram E, Cebesoy Ş, Solmaz S. Spectrum and symmetries of the impulsive difference equations. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70:38–51.
MLA	Bayram, Elgiz et al. “Spectrum and Symmetries of the Impulsive Difference Equations”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 70, no. 1, 2021, pp. 38-51, doi:10.31801/cfsuasmas.669708.
Vancouver	Bayram E, Cebesoy Ş, Solmaz S. Spectrum and symmetries of the impulsive difference equations. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70(1):38-51.