On the stability and boundedness of certain third order non-autonomous differential equations of retarded type

• Autores: Cemil Tunç
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 34, Nº. 2, 2015, págs. 147-159
• Idioma: inglés
• DOI: 10.4067/S0716-09172015000200004
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• Resumen

  • In this paper, based on the Lyapunov-Krasovskii functional approach, we obtain sufficient conditions which guarantee stability, uniformly stability, boundedness and uniformly boundedness of solutions of certain third order non- autonomous differential equations of retarded type. Our results complement and improve some recent ones.

• Referencias bibliográficas
  • Citas [1] Adams, D. O.; Omeike, M. O.; Mewomo, O. T.; Olusola, I. O., Boundedness of solutions of some third order non-autonomous ordinary...
  • [2] Ademola, T. A.; Arawomo,P. O., Asymptotic behaviour of solutions of third order nonlinear differential equations. Acta Univ. Sapientiae...
  • [3] Afuwape, A. U.; Adesina, O. A., On the bounds for mean-values of solutions to certain third-order non-linear differential equations. Fasc....
  • [4] Ahmad, S.; Rama Mohana Rao, M., Theory of ordinary differential equations. With applications in biology and engineering. Affiliated East-West...
  • [5] Bai, Yuzhen; Guo, C., New results on stability and boundedness of third order nonlinear delay differential equations. Dynam.Systems Appl....
  • [6] Burton, T. A., Stability and Periodic Solutions of Ordinary and Functional Differential Equations. Academic Press, Orlando, (1985).
  • [7] Chlouverakis, K. E.; Sprott, J. C., Chaotic hyperjerk systems. Chaos Solitons Fractals 28, No. 3, pp. 739-746, (2006).
  • [8] Cronin-Scanlon, J., Some mathematics of biological oscillations. SIAM Rev. 19, No. 1, pp. 100-138, (1977).
  • [9] Eichhorn, R.; Linz, S. J.; Hänggi, P., Transformations of nonlinear dynamical systems to jerky motion and its application to minimal chaotic...
  • [10] Elhadj, Z.; Sprott, J. C., Boundedness of certain forms of jerky dynamics. Qual. Theory Dyn.Syst. 11, No. 2, pp. 199-213, (2012).
  • [11] El-Nahhas, A., Stability of a third-order differential equation of retarded type. Appl. Math. Comput. 60, No. 2-3, pp. 147-152, (1994).
  • [12] El’sgol’ts, L. E., Introduction to the theory of dìfferential equations with deviating arguments. Translated from the Russian by Robert...
  • [13] Krasovskii, N. N., Stability of motion. Applications of Liapunov’s second method to differential systems and equations with delay. Stanford,...
  • [14] Linz, S. J., Onhyperjerky systems. Chaos Solitons Fractals 37, No. 3, pp. 741-747, (2008).
  • [15] Ogundare, B. S.; Okecha, G.E., On the boundedness and the stability of solution to third order non-linear differential equations. Ann....
  • [16] Rauch, L. L., Oscillation of a third order nonlinear autonomous system. Contributions to the Theory of Nonlinear Oscillations, pp. 39-88....
  • [17] Reissig, R.; Sansone, G.; Conti, R., Non-linear differential equations of higher order. Translated from the German. Noordhoff International...
  • [18] Sadek, A. I., On the stability of solutions of some non-autonomous delay differential equations of the third order. Asymptot. Anal. 43,no....
  • [19] Smith, H., An introduction to delay differential equations with applications to the life sciences. Texts in Applied Mathematics, 57....
  • [20] Tun¸c, C., Uniform ultimate boundedness of the solutions of third-order nonlinear differential equations. Kuwait J. Sci. Engrg. 32, No....
  • [21] Tun¸c, C., On the stability of solutions to a certain fourth-order delay differential equation. Nonlinear Dynam. 51(2008), No. 1-2, pp....
  • [22] Tun¸c, C., On the stability and boundedness of solutions to third order nonlinear differential equations with retarded argument. Nonlinear...
  • [23] Tun¸c, C., Bound of solutions to third-order nonlinear differential equations with bounded delay. J. Franklin Inst. 347, No. 2, pp. 415-425,...
  • [24] Tun¸c, C., On the stability and boundedness of solutions of nonlinear third order differential equations with delay. Filomat 24, No....
  • [25] Tun¸c, C., On the qualitative behaviors of solutions of some differential equations of higher order with multiple deviating arguments....
  • [26] Tun¸c, C., Stability and boundedness of the nonlinear differential equations of third order with multiple deviating arguments. Afr. Mat....
  • [27] Tun¸c, C., Stability and boundedness for a kind of non-autonomous differential equations with constant delay. Appl. Math. Inf. Sci. 7,...
  • [28] Yoshizawa,T., Stability theory by Liapunov’s second method. Publications of the Mathematical Society of Japan, No. 9. The Mathematical...
  • [29] Zhang, Lijuan; Yu, Lixin, Global asymptotic stability of certain thirdorder nonlinear differential equations. Math.Methods Appl. Sci....