Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2021, Cilt: 70 Sayı: 1, 38 - 51, 30.06.2021
https://doi.org/10.31801/cfsuasmas.669708

Öz

Kaynakça

  • 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

Yıl 2021, Cilt: 70 Sayı: 1, 38 - 51, 30.06.2021
https://doi.org/10.31801/cfsuasmas.669708

Öz

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 $\ell_{2}(\Z)$.

Kaynakça

  • 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.
Toplam 17 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Research Article
Yazarlar

Elgiz Bayram 0000-0003-2075-5016

Şerifenur Cebesoy 0000-0003-3571-6386

Seyda Solmaz 0000-0001-7572-2655

Yayımlanma Tarihi 30 Haziran 2021
Gönderilme Tarihi 3 Ocak 2020
Kabul Tarihi 15 Ağustos 2020
Yayımlandığı Sayı Yıl 2021 Cilt: 70 Sayı: 1

Kaynak Göster

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. Haziran 2021;70(1):38-51. doi:10.31801/cfsuasmas.669708
Chicago Bayram, Elgiz, Şerifenur Cebesoy, ve Seyda Solmaz. “Spectrum and Symmetries of the Impulsive Difference Equations”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70, sy. 1 (Haziran 2021): 38-51. https://doi.org/10.31801/cfsuasmas.669708.
EndNote Bayram E, Cebesoy Ş, Solmaz S (01 Haziran 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, ve S. Solmaz, “Spectrum and symmetries of the impulsive difference equations”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 70, sy. 1, ss. 38–51, 2021, doi: 10.31801/cfsuasmas.669708.
ISNAD Bayram, Elgiz vd. “Spectrum and Symmetries of the Impulsive Difference Equations”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70/1 (Haziran 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 vd. “Spectrum and Symmetries of the Impulsive Difference Equations”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 70, sy. 1, 2021, ss. 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.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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