Boundedness and square integrability of solutions of certain third-order differential equations
Djamila Beldjerd; Moussadek Remili
Mathematica Bohemica (2018)
- Volume: 143, Issue: 4, page 377-389
- ISSN: 0862-7959
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topBeldjerd, Djamila, and Remili, Moussadek. "Boundedness and square integrability of solutions of certain third-order differential equations." Mathematica Bohemica 143.4 (2018): 377-389. <http://eudml.org/doc/294229>.
@article{Beldjerd2018,
abstract = {We establish some new sufficient conditions which guarantee the boundedness and square integrability of solutions of certain third order differential equation. Example is included to illustrate the results. By this work, we extend and improve some results in the literature.},
author = {Beldjerd, Djamila, Remili, Moussadek},
journal = {Mathematica Bohemica},
keywords = {third-order differential equation; boundedness; square integrability},
language = {eng},
number = {4},
pages = {377-389},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Boundedness and square integrability of solutions of certain third-order differential equations},
url = {http://eudml.org/doc/294229},
volume = {143},
year = {2018},
}
TY - JOUR
AU - Beldjerd, Djamila
AU - Remili, Moussadek
TI - Boundedness and square integrability of solutions of certain third-order differential equations
JO - Mathematica Bohemica
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 143
IS - 4
SP - 377
EP - 389
AB - We establish some new sufficient conditions which guarantee the boundedness and square integrability of solutions of certain third order differential equation. Example is included to illustrate the results. By this work, we extend and improve some results in the literature.
LA - eng
KW - third-order differential equation; boundedness; square integrability
UR - http://eudml.org/doc/294229
ER -
References
top- Afuwape, A. U., Further ultimate boundedness results for a third-order non-linear system of differential equations, Boll. Unione Mat. Ital., VI. Ser., C, Anal. Funz. Appl. 4 (1985), 347-361. (1985) Zbl0592.34024MR0805225
- Afuwape, A. U., Omeike, M. O., Further ultimate boundedness of solutions of some system of third order nonlinear ordinary differential equations, Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., Math. 43 (2004),7-20. (2004) Zbl1068.34052MR2124598
- Èl’sgol’ts, L. È., Introduction to the Theory of Differential Equations With Deviating Arguments, Translated from the Russian by Robert J. McLaughlin. Holden-Day, San Francisco-London-Amsterdam (1966). (1966) Zbl0133.33502MR0192154
- Graef, J. R., Beldjerd, D., Remili, M., On stability, ultimate boundedness, and existence of periodic solutions of certain third order differential equations with delay, Panam. Math. J. 25 (2015), 82-94. (2015) Zbl1331.34145MR3364326
- Graef, J. R., Oudjedi, L. D., Remili, M., Stability and square integrability of solutions of nonlinear third order differential equations, Dyn. Contin. Discrete Impuls. Syst., Ser. A, Math. Anal. 22 (2015), 313-324. (2015) Zbl1326.34088MR3405345
- Omeike, M., Stability and boundedness of solutions of some non-autonomous delay differential equation of the third order, An. Ştiinţ. Univ. Al. I. Cuza Iaşi, Ser. Nouă, Mat. 55 (2009), 49-58. (2009) Zbl1199.34390MR2510712
- Omeike, M. O., 10.7153/dea-02-04, Differ. Equ. Appl. 2 (2010), 39-51. (2010) Zbl1198.34085MR2654750DOI10.7153/dea-02-04
- Omeike, M. O., New results on the stability of solution of some non-autonomous delay differential equations of the third order, Differ. Uravn. Protsessy Upr. (2010), 18-29. (2010) MR2766411
- Qian, C., 10.1016/S0362-546X(99)00120-0, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 42 (2000), 651-661. (2000) Zbl0969.34048MR1776296DOI10.1016/S0362-546X(99)00120-0
- Qian, C., 10.1016/S0022-247X(03)00302-0, J. Math. Anal. Appl. 284 (2003), 191-205. (2003) Zbl1054.34078MR1996127DOI10.1016/S0022-247X(03)00302-0
- Reissig, R., Sansone, G., Conti, R., Non-linear Differential Equations of Higher Order, Monographs and Textbooks on Pure and Applied Mathematics. Noordhoff International Publishing, Leyden (1974). (1974) Zbl0275.34001MR0344556
- Remili, M., Beldjerd, D., 10.1007/s12215-014-0169-3, Rend. Circ. Mat. Palermo (2) 63 (2014), 447-455. (2014) Zbl1321.34097MR3298595DOI10.1007/s12215-014-0169-3
- Remili, M., Beldjerd, D., A boundedness and stability results for a kind of third order delay differential equations, Appl. Appl. Math. 10 (2015), 772-782. (2015) Zbl1331.34135MR3447611
- Remili, M., Beldjerd, D., On ultimate boundedness and existence of periodic solutions of kind of third order delay differential equations, Acta Univ. M. Belii, Ser. Math. 24 (2016), 43-57. (2016) Zbl06699479MR3492940
- Remili, M., Beldjerd, D., 10.1016/j.jaubas.2016.05.002, Journal of the Association of Arab Universities for Basic and Applied Sciences 23 (2017), 90-95. (2017) MR3447611DOI10.1016/j.jaubas.2016.05.002
- Remili, M., Oudjedi, D. L., Stability and boundedness of the solutions of non autonomous third order differential equations with delay, Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., Math. 53 (2014), 139-147. (2014) Zbl1317.34157MR3331011
- Remili, M., Oudjedi, L. D., Uniform stability and boundedness of a kind of third order delay differential equations, Bull. Comput. Appl. Math. 2 (2014), 25-35. (2014) MR3569688
- Remili, M., Oudjedi, L. D., Boundedness and stability in third order nonlinear differential equations with bounded delay, An. Univ. Oradea, Fasc. Mat. 23 (2016), 135-143. (2016) Zbl1349.34303MR3496022
- Remili, M., Oudjedi, L. D., 10.5817/AM2016-2-79, Arch. Math., Brno 52 (2016), 79-90. (2016) Zbl06644060MR3535630DOI10.5817/AM2016-2-79
- Remili, M., Oudjedi, L. D., 10.1515/ausm-2016-0009, Acta Univ. Sapientiae, Math. 8 (2016), 150-165. (2016) Zbl1351.34087MR3535706DOI10.1515/ausm-2016-0009
- Sadek, A. I., On the stability of solutions of some non-autonomous delay differential equations of the third order, Asymptotic Anal. 43 (2005), 1-7. (2005) Zbl1075.34075MR2148124
- Tunç, C., On asymptotic stability of solutions to third order nonlinear differential equations with retarded argument, Commun. Appl. Anal. 11 (2007), 515-528. (2007) Zbl1139.34054MR2368199
- Tunç, C., Stability and boundedness of solutions of nonlinear differential equations of third-order with delay, Differ. Uravn. Protsessy Upr. (2007), 13 pages. (2007) MR2384532
- Tunç, C., 10.1007/s11071-008-9423-6, Nonlinear Dyn. 57 (2009), 97-106. (2009) Zbl1176.34064MR2511159DOI10.1007/s11071-008-9423-6
- Tunç, C., Some stability and boundedness conditions for non-autonomous differential equations with deviating arguments, Electron. J. Qual. Theory Differ. Equ. 2010 (2010), paper No. 1, 12 pages. (2010) Zbl1201.34123MR2577154
- Tunç, C., The boundedness of solutions to nonlinear third order differential equations, Nonlinear Dyn. Syst. Theory 10 (2010), 97-102. (2010) Zbl1300.34077MR2643196
- Tunç, C., Gözen, M., 10.1155/2013/248717, Abstr. Appl. Anal. 2013 (2013), Article ID 248717, 7 pages. (2013) Zbl1276.34058MR3055944DOI10.1155/2013/248717
- Zhu, Y., On stability, boundedness and existence of periodic solution of a kind of third order nonlinear delay differential system, Ann. Differ. Equations 8 (1992), 249-259. (1992) Zbl0758.34072MR1190138
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