A NEW INSTABILITY RESULT ON THE SOLUTIONS OF NONLINEAR VECTOR DIFFERENTIAL EQUATIONS OF THE FIFTH ORDER

Yıl 2015, Cilt: 8 Sayı: 2, 248 - 258, 06.04.2015

Melike Karta

https://doi.org/10.18185/eufbed.74815

Öz

The purpose of this paper is to investigate instability of the trivial solution of non-linear vector differential equation of the fifth order by constructing a Lyapunov function to get a new instability result and also to give an example indicate the importance of the topic. Related to a scalar differential equation mentioned in the literature, the findings of this study are beneficial for result of instability of the trivial solution of five order non-linear vectoral differential equations.

Anahtar Kelimeler

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BEŞINCI MERTEBEDEN LİNEER OLMAYAN VEKTÖR DIFERENSIYEL DENKLEMLERİN ÇÖZÜMLERİNİN KARARSIZLIĞI ÜZERINE YENİ BİR SONUÇ

Öz

Bu makalede, reel öklid uzayında

Anahtar Kelimeler

Kararsızlık, Krasovskii kriteri, Lyapunov’un ikinci

Kaynakça

• Ezeilo, J. O. C., 1978. Instability theorems for certain fifth-order differential equations. Math. Proc. Cambridge Philos. Soc., 84(2), 343- 350.
• Ezeilo, J. O. C., 1979. A further instability theorem for a certain fifth- order differential equation. Math. Proc. Cambridge Philos. Soc., 86(3), 491-493.
• Tiryaki, A., 1987. Extension of an instability theorem for a certain fifth order differential equation. National Mathematics Symposium, J. Karadeniz Tech. Univ. Fac.Arts Sci. Ser. Math. Phys., 11, Trabzon, 225- 227,
• Li, W. J., Yu, Y. H., 1990. Instabilitiy theorems for some fourth-order and fifth-order differential equations. (Chinese) J. Xinjiang Univ. Natur. Sci., 7(2), 7-10.
• Li, W., Duan, K., 2000. Instability theorems for some nonlinear differential systems of fifth order. (Chinese) J. Xinjiang Univ. Natur. Sci., 17(3), 1-5.
• Sadek, A.I., 2003. Instability results for certain systems of fourth and fifth order differential equations. Appl . Math. Comput., 145(2-3), 541-549.
• Tunç, C., 2004. On the instability of solutions of certain nonlinear vector differential equations of fifth order. Panamer. Math. J., 14(4), 25- 30.
• Tunç, C., 2005. An instability result for a certain non-autonomous vector differential equation of fifth-order. Panamer. Math. J., 15(3), 51- 58.
• Tunç, C., Şevli, H., 2005. On the instability of solutions of certain fifth order nonlinear differential equations. Mem. Differential Equations Math. Phys., 35, 147-156.
• Tunç, C., 2008. Further results on the instability of solutions of certain nonlinear vector differential equations of fifth order. Appl. Math. Inf. Sci ., 2(1) , 51-60.
• Tunç, C., Karta, M., 2008. A new instability result to nonlinear vector differential equations of fifth order. Discrete Dynamics in Nature and Society., 2008, doi:10.1155/2008/971534.
• Tunç, C., 2004. An ınstability theorem for a certain vector differential equation of the fourth order. Journal of Inequalities in Pure and Applied Mathematics.,5(1),1-5.
• Tunç, C., 2007. Some ınstability results on certain third order nonlinear vector differential equations Bulletin of the Institute of Mathematics Academia Sinica(new series).2(1), 109-122.
• Tunç,C., Erdoğan,F., 2007. On the instability of solutions of certain non- autonomous vector differential equations of fifth order. Sut J.Math. 43(1),35-38.
• Tunç, C., 2008. Further results on the ınstability of solutions of certain nonlinear vector differential equations of fifth order. Appl. Math.Inf. Sci. 2(1), 51-60.
• Tunç, C., 2011. A ınstability theorem for a certain fifth order delay differential equation, Filomat 25(3), 145-151.
• Tunç, C., 2011. On the instability of solutions of some fifth order nonlinear delay differential equations. Appl. Math. Inf. Sci.5(1), 112- 121.
• Tunç, C., 2012. Instability of non linear functional differential equations of fifth order. ITB J.Sci. 44(3), 239-249.
• Tunç, C., 2013. Instability to nonlinear vector differential equations of fifth order with constant delay.J.Math.Appl.36,121-130.
• Tunç, C., 2013.Instability of a fifth ordernon linear vector delay differential equation with multiple deviating arguments. U.P.B.Sci. Bull., Series A.76(1), 155-162.
• Krasovskii, N. N., 1955. On conditions of inversion of A.M. Lyapunov's theorems on instability for stationary systems of differential equations. (Russian) Doklady Akademii Nauk SSSR., 101,17- 20.
• Lyapunov, A. M., 1966. Stability of Motion. Academic Press, New York-London, 203p.
• Horn, R. A., Johnson, C.R., 1994. Topics in Matrix Analysis. Cambridge University Press, Cambridge, UK.