On the asymptotic behaviour of solutions of certain differential equations of the third order

• Ademola, A. T. ^[1] ; Arawomo, Peter Olutola ^[1]
  1. [1] University of Ibadan

     University of Ibadan

     Nigeria

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 33, Nº. 1, 2014, págs. 101-122
• Idioma: inglés
• DOI: 10.4067/S0716-09172014000100008
• Enlaces
  • Texto completo
• Resumen

  • In this article, Lyapunov second method is used to obtain criteria for uniform ultimate boundedness and asymptotic behaviour of solutions of nonlinear differential equations of the third order. The results obtained in this investigation include and extend some well known results on third order nonlinear differential equations in the literature.

• Referencias bibliográficas
  • Citas [1] Ademola, A. T. and Arawomo, P. O.; Boundedness and stability of‏ solutions of some nonlinear differential equations of the third...
  • [2] Ademola, A. T. and Arawomo, P. O.; On the stability and ultimate‏ boundedness of solutions for certain third order differential equations.‏...
  • [3] Ademola, A. T. and Arawomo, P. O.; Stability and ultimate boundedness of solutions to certain third order differential equations. Applied‏...
  • [4] Ademola, A. T. and Arawomo, P. O.; Stability and uniform ultimate‏ boundedness of solutions of some third order differential equations.‏...
  • [5] Ademola, A. T., Ogundiran, M.O., Arawomo, P.O. and Adesina, O.A.;‏ Boundedness results for a certain third order nonlinear differential‏...
  • [6] Ademola, A. T., Ogundiran, M.O., Arawomo, P.O. and Adesina, O.A.;‏ Stability results for the solutions of a certain third order nonlinear‏...
  • [7] Afuwape, A. U. and Adesina, O.A.; On the bounds for mean-values of‏ solutions to certain third order nonlinear differential equations,...
  • [8] Afuwape, A. U. and Omeike, M.O.; Convergence of solutions for certain non-homogeneous third order differential equations. Kragujevac‏...
  • [9] Chukwu, E. N.; On boundedness of solutions of third order differential‏ equations, Ann. Mat. Pura. Appl., 104, (4), pp. 123-149, (1975).‏
  • [10] Ezeilo, J. O. C.; A note on a boundedness theorem for some third order‏ differential equations, J. London Math. Soc., 36, pp. 439-444,...
  • [11] Ezeilo, J. O. C.; A boundedness theorem for a certain third order‏ differential equation, Proc. London Math. Soc. (3), 13, pp. 99-124,‏...
  • [12] Ezeilo, J. O. C.; A generalization of a boundedness theorem for the‏ equation x+αx ¨+φ2(x ˙)+φ3(x) = ψ(t, x, x, ˙ x ¨),...
  • [13] Ezeilo, J. O. C.; A generalization of some boundedness results by Reissig and Tejumola, J. Math. Anal. Appl., 41, pp. 411-419, (1973).‏
  • [14] Ezeilo, J. O. C. and Tejumola, H.O.; Boundedness theorems for certain‏ third order differential equations, Atti. Accad. Naz. Lincei Rend....
  • [15] Ezeilo, J. O. C.; Further results for the solutions of a third order‏ differential equation, Proc. Camb. Phil. Soc., 59, pp. 111-116,...
  • [16] Lakshmikantham, V. and Leels, S.; Ordinary differential and integral‏ inequalities: Theory and applications Vol. 1 Academic Press New...
  • [17] Nakashima, M.; Asymptotic behaviour of solutions of some third order‏ differential equations. Rep. Fac. Sci. Kagoshima Uni. (Math. Phys.‏...
  • [18] Ogundare, B. S.; On the convergence of solutions of certain third order‏ nonlinear differential equation, Math.Sci. Res. J. 9 (11), pp....
  • [19] Omeike, M. O.; New results on the asymptotic behaviour of a third‏ order nonlinear differential equations, Differential Equations &...
  • [20] Qian, C.; Asymptotic behaviour of a third order nonlinear differential‏ equation, J. Math. Anal. Appl., 284, no.1, pp. 191-205, (2003).‏
  • [21] Reissig, R., Sansone, G. and Conti, R.; Nonlinear differential equations‏ of higher order, Noordhoff International Publishing Leyeden,...
  • [22] Rouche, N., Habets, N. and Laloy, M.; Stability theory by Liapunov’s‏ direct method. Applied Mathematical Sciences 22, Springer-Verlag‏...
  • [23] Swick, K. E.; Asymptotic behaviour of the solutions of certain third‏ order differential equations, SIAM J. Appl., 19, N0. 1, pp. 96-102,‏...
  • [24] Swick, K. E.; On the boundedness and the stability of solutions for‏ some non-autonomous differential equations of the third order, J....
  • [25] Tejumola, H. O.; A note on the boundedness of solutions of some‏ nonlinear differential equations of the third order, Ghana J. of Science,‏...
  • [26] Tunc, C.; Boundedness of solutions of a third order nonlinear differential equation, J. Inequal. Pure and Appl. Math., 6 (1), pp. 1-6,...
  • [27] Tunc, C.; On the asymptotic behaviour of solutions of certain third‏ order nonlinear differential equations, J. Applied Math. and Stochastic‏...
  • [28] Tunc, E.; On the convergence of solutions of certain third order differential equations. Discrete Dyn. Nature and Society., pp. 1-12,...
  • [29] Yoshizawa, T.; Stability theory by Liapunov’s second method, The‏ Mathematical Society of Japan (1966)‏.