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Title: Boundedness of Solutions of Certain System of Second-order Ordinary Differential Equations (English)
Author: Omeike, M. O.
Author: Oyetunde, O. O.
Author: Olutimo, A. L.
Language: English
Journal: Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
ISSN: 0231-9721
Volume: 53
Issue: 1
Year: 2014
Pages: 107-115
Summary lang: English
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Category: math
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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. (English)
Keyword: boundedness
Keyword: Lyapunov function
Keyword: differential equations of second-order
MSC: 34C11
idZBL: Zbl 06416945
idMR: MR3331074
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Date available: 2014-09-01T08:12:37Z
Last updated: 2020-01-05
Stable URL: http://hdl.handle.net/10338.dmlcz/143919
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Reference: [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. MR 0721235, 10.1016/0022-247X(83)90243-3
Reference: [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
Reference: [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
Reference: [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. Zbl 0173.10302, MR 0212298, 10.1016/0022-247X(67)90035-2
Reference: [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. MR 0203144, 10.1007/BF02414336
Reference: [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. Zbl 0126.30403, MR 0173831, 10.1007/BF02412444
Reference: [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. MR 0204787, 10.1007/BF02416460
Reference: [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
Reference: [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. MR 1231497, 10.1006/jmaa.1993.1273
Reference: [10] Rao, M. R. M.: Ordinary differential equations. Affiliated East-West Private Limited, London, 1980. Zbl 0482.34001
Reference: [11] Reissig, R., Sansone, G., Conti, R.: Nonlinear Differential Equations of Higher Order. Noordhoff, Groningen, 1974.
Reference: [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. MR 0262597, 10.1007/BF02411167
Reference: [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. Zbl 0235.34081, MR 0306619
Reference: [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. Zbl 0374.34035, MR 0473341
Reference: [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. Zbl 0936.34041, MR 1695688
Reference: [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. Zbl 1162.34043, MR 2498299, 10.1016/j.na.2008.03.002
Reference: [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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