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Submitted
February 18, 2015
Accepted
May 2, 2016
Published
May 3, 2016
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Abstract

This paper establishes certain sufficient conditions to guarantee the non-existence of periodic solutions for a class of nonlinear vector differential equations of fifth order. With this work, we extend and improve two related results in the literature from scalar cases to vectorial cases. An example is given to illustrate the theoretical analysis made in this paper.

DOI : http://dx.doi.org/10.22342/jims.22.1.249.83-91

Keywords

Instability Lyapunov function nonlinear vector differential equation fifth order.

Article Details

How to Cite
Tunc, C., & Ates, M. (2016). INSTABILITY OF CERTAIN NONLINEAR DIFFERENTIAL EQUATIONS OF FIFTH ORDER. Journal of the Indonesian Mathematical Society, 22(1), 83–91. https://doi.org/10.22342/jims.22.1.249.83-91
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References

  1. Ezeilo, J. O. C., Instability theorems for certain fifth-order differential equations. Math. Proc. Cambridge Philos. Soc., no. 2, 84 (1978), 343–350.
  2. Ezeilo, J. O. C., Extension of certain instability theorems for some fourth and fifth order differential equations. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 66 (1979), no. 4, 239–242.
  3. Ezeilo, J. O. C., A further instability theorem for a certain fifth-order differential equation. Math. Proc. Cambridge Philos. Soc., no. 3, 86 (1979), 491–493.
  4. Horn, R. A.; Johnson, C. R., Topics in matrix analysis. Cambridge University Press, Cambridge, 1994.
  5. Krasovskii, N., On conditions of inversion of A. M. Lyapunov's theorems on instability for stationary systems of differential equations (Russian), Dokl. Akad. Nauk. SSSR (N.S.), 101, (1955), 17–20.
  6. Li, Wen-jian; Duan, Kui-chen, Instability theorems for some nonlinear differential systems of fifth order. J. Xinjiang Univ. Natur. Sci. 17 (2000), no. 3, 1–5, 18.
  7. Li, W. J.; Yu, Y. H., Instability theorems for some fourth-order and fifth-order differential equations, (Chinese) J. Xinjiang Univ. Natur. Sci., no. 2, 7 (1990), 7–10.
  8. Sadek, A. I., Instability results for certain systems of fourth and fifth order differential equations. Appl. Math. Comput. 145 (2003), no. 2–3, 541–549.
  9. Sun, Wu Jun; Hou, Xia New results about instability of some fourth and fifth order nonlinear systems. (Chinese) J. Xinjiang Univ. Natur. Sci. 16 (1999), no. 4, 14–17.
  10. Tejumola, H. O., Integral conditions of existence and non-existence of periodic solutions of some sixth and fifth order ordinary differential equations. J. Nigerian Math. Soc. 31 (2012), 23–33.
  11. Tunc, C., On the instability of solutions of certain nonlinear vector differential equations of fifth order. Panamer. Math. J. 14 (2004), no. 4, 25–30.
  12. Tunc, C., An instability result for a certain non-autonomous vector differential equation of fifth order. Panamer. Math. J. 15 (2005), no. 3, 51–58.
  13. Tunc, C., Further results on the instability of solutions of certain nonlinear vector differential equations of fifth order. Appl. Math. Inf. Sci. 2 (2008), no. 1, 51–60.
  14. Tunc, C., Instability of solutions for certain nonlinear vector differential equations of fourth order. Nelīnīĭnī Koliv. 12 (2009), no. 1, 120-129; translation in Nonlinear Oscil. (N. Y.) 12 (2009), no. 1, 123–132.
  15. Tunc, C., Instability in multi delay functional differential equations of fourth order. Fasc. Math. 55 (2015), no.1, 189-198.
  16. Tunc, C.; Erdogan, F., On the instability of solutions of certain non-autonomous vector differential equations of fifth order. SUT J. Math. 43 (2007), no. 1, 35–48.
  17. Tunc, C.; Karta, M., A new instability result to nonlinear vector differential equations of fifth order. Discrete Dyn. Nat. Soc. 2008, Art. ID 971534, 6 pp.
  18. Tunc, C.; Şevli, H., On the instability of solutions of certain fifth order nonlinear differential equations. Mem. Differential Equations Math. Phys. 35 (2005), 147–156.