New result on the ultimate boundedness of solutions of certain third-order vector differential equations
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 49 (2010) no. 1, pp. 55-61 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Sufficient conditions are established for ultimate boundedness of solutions of certain nonlinear vector differential equations of third-order. Our result improves on Tunc’s [C. Tunc, On the stability and boundedness of solutions of nonlinear vector differential equations of third order].
Sufficient conditions are established for ultimate boundedness of solutions of certain nonlinear vector differential equations of third-order. Our result improves on Tunc’s [C. Tunc, On the stability and boundedness of solutions of nonlinear vector differential equations of third order].
Classification : 34B15, 34C11
Keywords: Ultimate boundedness; Lyapunov function; differential equation of third order
@article{AUPO_2010_49_1_a5,
     author = {Omeike, M. O. and Afuwape, A. U.},
     title = {New result on the ultimate boundedness of solutions of certain third-order vector differential equations},
     journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
     pages = {55--61},
     year = {2010},
     volume = {49},
     number = {1},
     mrnumber = {2797523},
     zbl = {1237.34045},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AUPO_2010_49_1_a5/}
}
TY  - JOUR
AU  - Omeike, M. O.
AU  - Afuwape, A. U.
TI  - New result on the ultimate boundedness of solutions of certain third-order vector differential equations
JO  - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY  - 2010
SP  - 55
EP  - 61
VL  - 49
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/AUPO_2010_49_1_a5/
LA  - en
ID  - AUPO_2010_49_1_a5
ER  - 
%0 Journal Article
%A Omeike, M. O.
%A Afuwape, A. U.
%T New result on the ultimate boundedness of solutions of certain third-order vector differential equations
%J Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
%D 2010
%P 55-61
%V 49
%N 1
%U http://geodesic.mathdoc.fr/item/AUPO_2010_49_1_a5/
%G en
%F AUPO_2010_49_1_a5
Omeike, M. O.; Afuwape, A. U. New result on the ultimate boundedness of solutions of certain third-order vector differential equations. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 49 (2010) no. 1, pp. 55-61. http://geodesic.mathdoc.fr/item/AUPO_2010_49_1_a5/

[1] Afuwape, A. U.: Ultimate boundedness results for a certain system of third-order nonlinear differential equations. J. Math. Anal. Appl. 97 (1983), 140–150. | DOI | MR

[2] Afuwape, A. U.: Further ultimate boundedness results for a third-order nonlinear system of differential equations. Analisi Funzionale e Appl. 6 (1985), 99–100, N.I. 348–360. | MR

[3] 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. rer. nat., Math. 43 (2004), 7–20. | MR

[4] Chukwu, E. N.: On the boundedness of solutions of third-order differential equations. Ann. Math. Pura Appl. 4 (1975), 123–149. | MR | Zbl

[5] Ezeilo, J. O. C.: n-dimensional extensions of boundedness and stability theorems for some third-order differential equations. J. Math. Anal. Appl. 18 (1967), 394–416. | DOI | MR | Zbl

[6] Ezeilo, J. O. C.: A generalization of a boundedness theorem for a certain third-order differential equation. Proc. Cambridge Philos. Soc. 63 (1967), 735–742. | MR

[7] Ezeilo, J. O. C.: On the convergence of solutions of certain system of second order equations. Ann. Math. Pura Appl. 72, 4 (1966), 239–252. | DOI | MR

[8] Ezeilo, J. O. C.: Stability results for the solutions of some third and fourth-order differential equations. Ann. Math. Pura Appl. 66, 4 (1964), 233–250. | DOI | MR | Zbl

[9] Ezeilo, J. O. C., Tejumola, H. O.: Boundedness and periodicity of solutions of a certain system of third-order nonlinear differential equations. Ann. Math. Pura Appl. 74 (1966), 283–316. | DOI | MR

[10] Ezeilo, J. O. C., Tejumola, H. O.: Further results for a system of third-order ordinary differential equations. Atti. Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 58 (1975), 143–151. | MR

[11] Liapunov, A. M.: Stability of Motion. Academic Press, London, 1966. | MR

[12] Meng, F. W.: Ultimate boundedness results for a certain system of third-order nonlinear differential equations. J. Math. Anal. Appl. 177 (1993), 496–509. | DOI | MR

[13] Rao, M. R. M.: Ordinary Differential Equations. Affiliated East-West Private Limited, London, 1980. | Zbl

[14] Reissig, R., Sansone, G., Conti, R.: Nonlinear Differential Equations of Higher Order. Noordhoff, Groningen, 1974.

[15] Tejumola, H. O.: A note on the boundedness and stability of solutions of certain third-order differential equations. Ann. Math. Pura Appl. 92, 4 (1972), 65–75. | DOI | MR

[16] Tejumola, H. O.: On the boundedness and periodicity of solutions of certain third-order nonlinear differential equation. Ann. Math. Pura Appl. 83, 4 (1969), 195–212. | DOI | MR

[17] Tiryaki, A.: Boundedness and periodicity results for a certain system of third-order nonlinear differential equations. Indian J. Pure Appl. Math. 30, 4 (1999), 361-372. | MR | Zbl

[18] Tunc, C.: Boundedness of solutions of a certain third-order nonlinear differential equations. J. Inequal. Pure and Appl. Math. 6, 1 (2005), Art 3 1–6.

[19] Tunc, C.: On the stability and boundedness of solutions of nonlinear vector differential equations of third order. Nonlinear Analysis 70, 6 (2009), 2232–2236. | DOI | MR | Zbl

[20] Tunc, C., Ates, M.: Stability and boundedness results for solutions of certain third order nonlinear vector differential equations. Nonlinear Dynam. 45, 3-4 (2006), 273–281. | DOI | MR | Zbl