# Article

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Keywords:
boundedness; Lyapunov function; differential equations of second-order
Summary:
We extend, in this paper, some known results on the boundedness of solutions of certain second order nonlinear scalar differential equations to system of second order nonlinear differential equations.
References:
[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 10.1016/0022-247X(83)90243-3 | MR 0721235
[2] Afuwape, A. U.: Further ultimate boundedness results for a third-order nonlinear system of differential equations. Analisi Funzionale e Appl. 6, 99-100, N.I. (1985), 348–360. MR 0805225
[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 2124598
[4] Ezeilo, J. O. C.: n-dimensional extensions of boundedness and stability theorems for some third-order differential equations. J. Math. Anal. Appl. 18 (1967), 395–416. DOI 10.1016/0022-247X(67)90035-2 | MR 0212298 | Zbl 0173.10302
[5] 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 10.1007/BF02414336 | MR 0203144
[6] 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 10.1007/BF02412444 | MR 0173831 | Zbl 0126.30403
[7] 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 10.1007/BF02416460 | MR 0204787
[8] 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 0425261
[9] 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 10.1006/jmaa.1993.1273 | MR 1231497
[10] Rao, M. R. M.: Ordinary differential equations. Affiliated East-West Private Limited, London, 1980. Zbl 0482.34001
[11] Reissig, R., Sansone, G., Conti, R.: Nonlinear Differential Equations of Higher Order. Noordhoff, Groningen, 1974.
[12] 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 10.1007/BF02411167 | MR 0262597
[13] Tejumola, H. O.: Boundedness criteria for solutions of some second order differential equations. Academia Nazionale Dei Lincei, Serie VII, 50, 4 (1971), 204–209. MR 0306619 | Zbl 0235.34081
[14] Tejumola, H. O.: On a Lienard type matrix differential equation. Atti. Accad. Naz. Lincei Rendi. Cl. Sci. Fis. Mat. Natur (8) 60, 2 (1976), 100–107. MR 0473341 | Zbl 0374.34035
[15] 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 1695688 | Zbl 0936.34041
[16] 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 10.1016/j.na.2008.03.002 | MR 2498299 | Zbl 1162.34043
[17] Yoshizawa, T.: On the evaluation of the derivatives of solutions of $y^{\prime \prime }=f(x,y,y^{\prime })$. Mem. Coll. Sci., Univ. Kyoto, Series A, Math. 28 (1953), 27–32, 133–141. MR 0060088

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