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SPECTRAL ANALYSIS OF BOUNDARY VALUE PROBLEMS WITH RETARDED ARGUMENT

Year 2017, Volume: 66 Issue: 2, 175 - 194, 01.08.2017
https://doi.org/10.1501/Commua1_0000000810

Abstract

In this paper, by modifying some techniques of [S.B. Norkin, Differential equations of the second order with retarded argument, Translations of Mathematical Monographs, Vol. 31, AMS, Providence, RI, 1972]and suggesting own approaches we find asymptotic formulas for the eigenvalues and eigen functions of boundary value problems of Sturm-Liouville type for the second order differential equation with retarded argument

References

  • Norkin, S.B., Diğerential equations of the second order with retarded argument, Translations of Mathematical Monographs, Vol. 31, AMS, Providence, RI, 1972.
  • Norkin, S.B., On boundary problem of Sturm-Liouville type for second-order diğ erential equa- tion with retarded argument, Izv. Vys´s. U´cebn. Zaved. Matematika, no 6(7) (1958) 203-214 (Russian).
  • Kamenskii, G. A., On the asymptotic behaviour of solutions of linear diğ erential equations of the second order with retarded argument, Uch. Zap. Mosk. Gos. Univ., 165 (1954) 195-204 (Russian).
  • Bayramo¼glu, M., K. Köklü, O. Baykal, On the spectral properties of the regular Sturm- Liouville Problem with the lag argument for which its boundary conditions depends on the spectral parameter, Turk. J. Math., 26 (2002) 421-431.
  • ¸Sen, E. and A. Bayramov, Asymptotic formulations of the eigenvalues and eigenfunctions for a boundary value problem, Math. Method. Appl. Sci., 36 (2013) 1512-1519.
  • ¸Sen, E. and A. Bayramov, Calculation of eigenvalues and eigenfunctions of a discontinuous boundary value problem with retarded argument which contains a spectral parameter in the
  • boundary condition, Math. Comput. Model., 54 (11-12) (2011) 3090-3097.
  • Bayramov, A., On asymptotic of the eigenvalues and eigenfunctions for the problem of Sturm- Liouville with the lag argument and the spectral parameter in the boundary condition, Trans. Acad. Sci. Azerb., Ser. Phys.-Tech. Math. Sci., 18 (3-4) (1998) 6-11.
  • Bayramov, A., S. C. alıs.kan and S. Uslu, Computation of eigenvalues and eigenfunctions of a discontinuous boundary value problem with retarded argument, Appl. Math. Comput., 191 (2007) 592-600.
  • Yang, C., Trace and inverse problem of a discontinuous Sturm–Liouville operator with re- tarded argument, J. Math. Anal. Appl., 395 (1) (2012) 30-41.
  • Levitan,B. M., Expansion in characteristic functions of diğerential equations of the second order, GITTL, Moscow, 1950 (Russian).
  • Bairamov, E., E. Ugurlu, On the characteristic values of the real component of a dissipative boundary value transmission problem, Appl. Math. Comput., 218 (2012) 9657-9663.
  • Bairamov, E., E, Ugurlu, E, The determinants of dissipative Sturm-Liouville operators with transmission conditions, Math. Comput. Model., 53 (5/6) (2011) 805-813.
  • Mamedov, Kh. R., On Boundary Value Problem with Parameter in Boundary Conditions, Spectral Theory of Operator and Its Applications, 11 (1997) 117-121 (Russian).
  • Fulton, C. and S. Pruess, Eigenvalue and eigenfunction asymptotics for regular Sturm- Liouville problems, J. Math. Anal. Appl., 188 (1) (1994) 297–340.
  • Aydemir, K., O. Sh. Mukhtarov, Variational principles for spectral analysis of one Sturm- Liouville problem with transmission conditions, Advances in Diğerence Equations, 2016 (2016) 1-14.
  • Mukhtarov, O. Sh., K. Aydemir, Eigenfunction expansion for Sturm-Liouville problems with transmission conditions at one interior point, Acta Mathematica Scientia, 35 (3) (2015) 639-649.
  • Mukhtarov, O. Sh., M. Kadakal, F. S. Muhtarov, On discontinuous Sturm-Liouville problems with transmission conditions, J. Math. Kyoto Univ., 44 (4) (2004) 779-798.
  • Kadakal, M., O. Sh. Mukhtarov, Discontinuous Sturm-Liouville problems containing eigen- parameter in the boundary conditions, 22 (5) (2006) 1519-1528.
  • Current address : Erdo¼gan ¸Sen: Department of Mathematics, Namık Kemal University, 59030, Tekirda¼g, Turkey
  • E-mail address : erdogan.math@gmail.com
  • Current address : Azad Bayramov: Azerbaijan State Pedagogical University, 1000, Baku, Azer- baijan
  • E-mail address : azadbay@gmail.com
Year 2017, Volume: 66 Issue: 2, 175 - 194, 01.08.2017
https://doi.org/10.1501/Commua1_0000000810

Abstract

References

  • Norkin, S.B., Diğerential equations of the second order with retarded argument, Translations of Mathematical Monographs, Vol. 31, AMS, Providence, RI, 1972.
  • Norkin, S.B., On boundary problem of Sturm-Liouville type for second-order diğ erential equa- tion with retarded argument, Izv. Vys´s. U´cebn. Zaved. Matematika, no 6(7) (1958) 203-214 (Russian).
  • Kamenskii, G. A., On the asymptotic behaviour of solutions of linear diğ erential equations of the second order with retarded argument, Uch. Zap. Mosk. Gos. Univ., 165 (1954) 195-204 (Russian).
  • Bayramo¼glu, M., K. Köklü, O. Baykal, On the spectral properties of the regular Sturm- Liouville Problem with the lag argument for which its boundary conditions depends on the spectral parameter, Turk. J. Math., 26 (2002) 421-431.
  • ¸Sen, E. and A. Bayramov, Asymptotic formulations of the eigenvalues and eigenfunctions for a boundary value problem, Math. Method. Appl. Sci., 36 (2013) 1512-1519.
  • ¸Sen, E. and A. Bayramov, Calculation of eigenvalues and eigenfunctions of a discontinuous boundary value problem with retarded argument which contains a spectral parameter in the
  • boundary condition, Math. Comput. Model., 54 (11-12) (2011) 3090-3097.
  • Bayramov, A., On asymptotic of the eigenvalues and eigenfunctions for the problem of Sturm- Liouville with the lag argument and the spectral parameter in the boundary condition, Trans. Acad. Sci. Azerb., Ser. Phys.-Tech. Math. Sci., 18 (3-4) (1998) 6-11.
  • Bayramov, A., S. C. alıs.kan and S. Uslu, Computation of eigenvalues and eigenfunctions of a discontinuous boundary value problem with retarded argument, Appl. Math. Comput., 191 (2007) 592-600.
  • Yang, C., Trace and inverse problem of a discontinuous Sturm–Liouville operator with re- tarded argument, J. Math. Anal. Appl., 395 (1) (2012) 30-41.
  • Levitan,B. M., Expansion in characteristic functions of diğerential equations of the second order, GITTL, Moscow, 1950 (Russian).
  • Bairamov, E., E. Ugurlu, On the characteristic values of the real component of a dissipative boundary value transmission problem, Appl. Math. Comput., 218 (2012) 9657-9663.
  • Bairamov, E., E, Ugurlu, E, The determinants of dissipative Sturm-Liouville operators with transmission conditions, Math. Comput. Model., 53 (5/6) (2011) 805-813.
  • Mamedov, Kh. R., On Boundary Value Problem with Parameter in Boundary Conditions, Spectral Theory of Operator and Its Applications, 11 (1997) 117-121 (Russian).
  • Fulton, C. and S. Pruess, Eigenvalue and eigenfunction asymptotics for regular Sturm- Liouville problems, J. Math. Anal. Appl., 188 (1) (1994) 297–340.
  • Aydemir, K., O. Sh. Mukhtarov, Variational principles for spectral analysis of one Sturm- Liouville problem with transmission conditions, Advances in Diğerence Equations, 2016 (2016) 1-14.
  • Mukhtarov, O. Sh., K. Aydemir, Eigenfunction expansion for Sturm-Liouville problems with transmission conditions at one interior point, Acta Mathematica Scientia, 35 (3) (2015) 639-649.
  • Mukhtarov, O. Sh., M. Kadakal, F. S. Muhtarov, On discontinuous Sturm-Liouville problems with transmission conditions, J. Math. Kyoto Univ., 44 (4) (2004) 779-798.
  • Kadakal, M., O. Sh. Mukhtarov, Discontinuous Sturm-Liouville problems containing eigen- parameter in the boundary conditions, 22 (5) (2006) 1519-1528.
  • Current address : Erdo¼gan ¸Sen: Department of Mathematics, Namık Kemal University, 59030, Tekirda¼g, Turkey
  • E-mail address : erdogan.math@gmail.com
  • Current address : Azad Bayramov: Azerbaijan State Pedagogical University, 1000, Baku, Azer- baijan
  • E-mail address : azadbay@gmail.com
There are 23 citations in total.

Details

Primary Language English
Journal Section Research Articles
Authors

Erdoğan Şen This is me

Azad Bayramov This is me

Publication Date August 1, 2017
Published in Issue Year 2017 Volume: 66 Issue: 2

Cite

APA Şen, E., & Bayramov, A. (2017). SPECTRAL ANALYSIS OF BOUNDARY VALUE PROBLEMS WITH RETARDED ARGUMENT. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 66(2), 175-194. https://doi.org/10.1501/Commua1_0000000810
AMA Şen E, Bayramov A. SPECTRAL ANALYSIS OF BOUNDARY VALUE PROBLEMS WITH RETARDED ARGUMENT. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. August 2017;66(2):175-194. doi:10.1501/Commua1_0000000810
Chicago Şen, Erdoğan, and Azad Bayramov. “SPECTRAL ANALYSIS OF BOUNDARY VALUE PROBLEMS WITH RETARDED ARGUMENT”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66, no. 2 (August 2017): 175-94. https://doi.org/10.1501/Commua1_0000000810.
EndNote Şen E, Bayramov A (August 1, 2017) SPECTRAL ANALYSIS OF BOUNDARY VALUE PROBLEMS WITH RETARDED ARGUMENT. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66 2 175–194.
IEEE E. Şen and A. Bayramov, “SPECTRAL ANALYSIS OF BOUNDARY VALUE PROBLEMS WITH RETARDED ARGUMENT”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 66, no. 2, pp. 175–194, 2017, doi: 10.1501/Commua1_0000000810.
ISNAD Şen, Erdoğan - Bayramov, Azad. “SPECTRAL ANALYSIS OF BOUNDARY VALUE PROBLEMS WITH RETARDED ARGUMENT”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66/2 (August 2017), 175-194. https://doi.org/10.1501/Commua1_0000000810.
JAMA Şen E, Bayramov A. SPECTRAL ANALYSIS OF BOUNDARY VALUE PROBLEMS WITH RETARDED ARGUMENT. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2017;66:175–194.
MLA Şen, Erdoğan and Azad Bayramov. “SPECTRAL ANALYSIS OF BOUNDARY VALUE PROBLEMS WITH RETARDED ARGUMENT”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 66, no. 2, 2017, pp. 175-94, doi:10.1501/Commua1_0000000810.
Vancouver Şen E, Bayramov A. SPECTRAL ANALYSIS OF BOUNDARY VALUE PROBLEMS WITH RETARDED ARGUMENT. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2017;66(2):175-94.

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

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