Yıl 2021,
Cilt: 70 Sayı: 1, 38 - 51, 30.06.2021
Elgiz Bayram
,
Şerifenur Cebesoy
,
Seyda Solmaz
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
Elgiz Bayram
,
Şerifenur Cebesoy
,
Seyda Solmaz
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.