Oscillation properties of second-order quasilinear difference equations with unbounded delay and advanced neutral terms

George E. Chatzarakis; Ponnuraj Dinakar; Srinivasan Selvarangam; Ethiraju Thandapani

Mathematica Bohemica (2022)

  • Volume: 147, Issue: 2, page 271-284
  • ISSN: 0862-7959

Abstract

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We obtain some new sufficient conditions for the oscillation of the solutions of the second-order quasilinear difference equations with delay and advanced neutral terms. The results established in this paper are applicable to equations whose neutral coefficients are unbounded. Thus, the results obtained here are new and complement some known results reported in the literature. Examples are also given to illustrate the applicability and strength of the obtained conditions over the known ones.

How to cite

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Chatzarakis, George E., et al. "Oscillation properties of second-order quasilinear difference equations with unbounded delay and advanced neutral terms." Mathematica Bohemica 147.2 (2022): 271-284. <http://eudml.org/doc/297668>.

@article{Chatzarakis2022,
abstract = {We obtain some new sufficient conditions for the oscillation of the solutions of the second-order quasilinear difference equations with delay and advanced neutral terms. The results established in this paper are applicable to equations whose neutral coefficients are unbounded. Thus, the results obtained here are new and complement some known results reported in the literature. Examples are also given to illustrate the applicability and strength of the obtained conditions over the known ones.},
author = {Chatzarakis, George E., Dinakar, Ponnuraj, Selvarangam, Srinivasan, Thandapani, Ethiraju},
journal = {Mathematica Bohemica},
keywords = {oscillation; quasilinear difference equation; delay and advanced neutral terms},
language = {eng},
number = {2},
pages = {271-284},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Oscillation properties of second-order quasilinear difference equations with unbounded delay and advanced neutral terms},
url = {http://eudml.org/doc/297668},
volume = {147},
year = {2022},
}

TY - JOUR
AU - Chatzarakis, George E.
AU - Dinakar, Ponnuraj
AU - Selvarangam, Srinivasan
AU - Thandapani, Ethiraju
TI - Oscillation properties of second-order quasilinear difference equations with unbounded delay and advanced neutral terms
JO - Mathematica Bohemica
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 147
IS - 2
SP - 271
EP - 284
AB - We obtain some new sufficient conditions for the oscillation of the solutions of the second-order quasilinear difference equations with delay and advanced neutral terms. The results established in this paper are applicable to equations whose neutral coefficients are unbounded. Thus, the results obtained here are new and complement some known results reported in the literature. Examples are also given to illustrate the applicability and strength of the obtained conditions over the known ones.
LA - eng
KW - oscillation; quasilinear difference equation; delay and advanced neutral terms
UR - http://eudml.org/doc/297668
ER -

References

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  1. Agarwal, R. P., 10.1201/9781420027020, Pure and Applied Mathematics, Marcel Dekker 228. Marcel Dekker, New York (2000). (2000) Zbl0952.39001MR1740241DOI10.1201/9781420027020
  2. Agarwal, R. P., Bohner, M., Grace, S. R., O'Regan, D., 10.1155/9789775945198, Hindawi Publishing, New York (2005). (2005) Zbl1084.39001MR2179948DOI10.1155/9789775945198
  3. Agarwal, R. P., Grace, S. R., n-Bohner, E. Akı, On the oscillation of higher order neutral difference equations of mixed type, Dyn. Syst. Appl. 11 (2002), 459-469. (2002) Zbl1046.39001MR1946136
  4. Chatzarakis, G. E., Miliaras, G. N., 10.1216/RMJ-2015-45-1-131, Rocky Mt. J. Math. 45 (2015), 131-156. (2015) Zbl1312.39018MR3334206DOI10.1216/RMJ-2015-45-1-131
  5. Chatzarakis, G. E., Miliaras, G. N., Stavroulakis, I. P., Thandapani, E., Asymptotic behaviour of non-oscillatory solutions of first-order neutral difference equations, Panam. Math. J. 23 (2013), 111-129. (2013) Zbl1280.39005MR3075268
  6. Grace, S. R., 10.1006/jmaa.1998.6001, J. Math. Anal. Appl. 224 (1998), 241-254. (1998) Zbl0911.39006MR1637453DOI10.1006/jmaa.1998.6001
  7. Grace, S. R., Alzabut, J., 10.1186/s13662-019-2472-y, Adv. Difference Equ. 2020 (2020), Article ID 8, 12 pages. (2020) MR4048362DOI10.1186/s13662-019-2472-y
  8. Grace, S. R., Dontha, S., Oscillation of higher order neutral difference equations of mixed type, Dyn. Syst. Appl. 12 (2003), 521-532. (2003) Zbl1054.39004MR2020481
  9. Jiang, J., 10.1016/S0096-3003(02)00631-8, Appl. Math. Comput. 146 (2003), 791-801. (2003) Zbl1035.34074MR2008588DOI10.1016/S0096-3003(02)00631-8
  10. Saker, S. H., 10.1016/S0096-3003(02)00286-2, Appl. Math. Comput. 142 (2003), 99-111. (2003) Zbl1028.39003MR1978250DOI10.1016/S0096-3003(02)00286-2
  11. Seghar, D., Thandapani, E., Pinelas, S., 10.9734/BJMCS/2015/16079, Br. J. Math. Comput. Sci. 8 (2015), 121-133. (2015) MR3431692DOI10.9734/BJMCS/2015/16079
  12. Selvarangam, S., Geetha, S., Thandapani, E., Pinelas, S., Classification of solutions of second order nonlinear neutral difference equations of mixed type, Dyn. Contin. Discrete Impuls. Syst., Ser. B, Appl. Algorithms 23 (2016), 433-447. (2016) Zbl1355.39017
  13. Selvarangam, S., Thandapani, E., Pinelas, S., 10.1186/1029-242X-2014-417, J. Inequal. Appl. 2014 (2014), Article ID 417, 15 pages. (2014) Zbl1332.39005MR3347707DOI10.1186/1029-242X-2014-417
  14. Sun, Y. G., Saker, S. H., 10.1016/j.amc.2004.04.017, Appl. Math. Comput. 163 (2005), 909-918. (2005) Zbl1078.39014MR2121836DOI10.1016/j.amc.2004.04.017
  15. Thandapani, E., Balasubramanian, V., Oscillation and asymptotic behavior of second order nonlinear neutral difference equations of mixed arguments, Transylv. J. Math. Mech. 5 (2013), 149-156. (2013) MR3158542
  16. Thandapani, E., Balasubramanian, V., 10.7153/dea-05-19, Differ. Equ. Appl. 3 (2013), 319-330. (2013) Zbl1284.39012MR3136342DOI10.7153/dea-05-19
  17. Thandapani, E., Balasubramanian, V., Some oscillation theorems for second order nonlinear neutral type difference equations, Malaya J. Mat. 3 (2013), 34-43. (2013) Zbl1369.39009MR3136342
  18. Thandapani, E., Kavitha, N., Oscillation theorems for second-order nonlinear neutral difference equation of mixed type, J. Math. Comput. Sci. 1 (2011), 89-102. (2011) MR2913381
  19. Thandapani, E., Kavitha, N., Pinelas, S., Comparison and oscillation theorem for second-order nonlinear neutral difference equations of mixed type, Dyn. Syst. Appl. 21 (2012), 83-92. (2012) Zbl1280.39010MR2953239
  20. Thandapani, E., Kavitha, N., Pinelas, S., 10.1186/1687-1847-2012-4, Adv. Difference Equ. 2012 (2012), Article ID 4, 10 pages. (2012) Zbl1278.39016MR2897466DOI10.1186/1687-1847-2012-4
  21. Thandapani, E., Mahalingam, K., 10.5556/j.tkjm.34.2003.260, Tamkang J. Math. 34 (2003), 137-145. (2003) Zbl1044.39016MR1976332DOI10.5556/j.tkjm.34.2003.260
  22. Thandapani, E., Mahalingam, K., 10.1023/B:CMAJ.0000024532.03496.b2, Czech. Math. J. 53 (2003), 935-947. (2003) Zbl1080.39503MR2018841DOI10.1023/B:CMAJ.0000024532.03496.b2
  23. Thandapani, E., Seghar, D., Selvarangam, S., Oscillation of second order quasilinear difference equations with several neutral terms, Transylv. J. Math. Mech. 7 (2015), 67-74. (2015) Zbl1345.39003MR3373908
  24. Thandapani, E., Selvarangam, S., Oscillation theorems for second order quasilinear neutral difference equations, J. Math. Comput. Sci. 2 (2012), 866-879. (2012) MR2947156
  25. Thandapani, E., Selvarangam, S., Oscillation of solutions of second order neutral type difference equations, Nonlinear Funct. Anal. Appl. 20 (2015), 329-336. (2015) Zbl1341.39003
  26. Thandapani, E., Sundaram, P., Gyori, I., Oscillation of second order nonlinear neutral delay difference equations, J. Math. Phys. Sci. 31 (1997), 121-132. (1997) MR1867518
  27. Wang, D.-M., Xu, Z.-T., 10.1007/s10255-011-0043-4, Acta Math. Appl. Sin., Engl. Ser. 27 (2011), 93-104. (2011) Zbl1242.39021MR2754764DOI10.1007/s10255-011-0043-4
  28. Zhang, S.-Y., Wang, Q.-R., 10.1016/j.amc.2010.03.134, Appl. Math. Comput. 216 (2010), 2837-2848. (2010) Zbl1218.34112MR2653099DOI10.1016/j.amc.2010.03.134

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