Instability to nonlinear vector differential equations of fifth order with constant delay

• Autorzy: Tunҫ C.

Identyfikatory

DOI

10.7862/rf.2013.11

• Języki publikacji: EN

Abstrakty

EN

We consider a certain vector differential equation of the fifth order with a constant delay. We give new certain sucient conditions which guarantee the instability of the zero solution of that equation. An example is given to illustrate the theoretical analysis made in the paper.

Słowa kluczowe

EN

vector differential equation; fifth order; instability; delay

PL

równanie różniczkowe; równanie różniczkowe piątego rzędu; niestabilność; opóźnienie

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2013
• Tom: Vol. 36
• Strony: 121--130
• Opis fizyczny: Bibliogr. 17 poz.

Twórcy

autor

Tunҫ C.

• Department of Mathematics, Faculty of Sciences, Yüzüncü Yıl University, 65080, Van, Turkey

Bibliografia

• [1] Bellman, R., Introduction to matrix analysis. Reprint of the second (1970) edition. With a foreword by Gene Golub. Classics in Applied Mathematics, 19. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1997.
• [2] Ezeilo, J. O.C., Instability theorems for certain fifth-order differential equations, Math. Proc. Cambridge Philos. Soc. 84 (1978), no. 2, 343-350.
• [3] Krasovskii, N. 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.
• [4] LaSalle, J.& Lefschetz, S., Stability by Liapunov's direct method with applications. Mathematics in Science and Engineering, Vol. 4, Academic Press, New York-London, 1961.
• [5] 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.
• [6] 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.
• [7] Tunҫ, 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.
• [8] Tunҫ, C., On the instability of solutions of some fifth order nonlinear delay differential equations, Appl. Math. Inf. Sci. (AMIS). 5 (2011), no.1, 112-121.
• [9] Tunҫ, C., An instability theorem for a certain fifth-order delay differential equation, Filomat 25:3 (2011), 145-151.
• [10] Tunҫ, C., Recent advances on instability of solutions of fourth and fifth order delay differential equations with some open problems. World Scientific Review, Vol. 9,World Scientific Series on Nonlinear Science Series B (Book Series), (2011), 105-116.
• [11] Tunҫ, C., On the instability of solutions of nonlinear delay differential equations of fourth and fifth order, Sains Malaysiana 40 (12), (2011), 1455-1459.
• [12] Tunҫ, C., Instability for nonlinear differential equations of fifth order subject to delay, Nonlinear Dyn. Syst. Theory 12 (2) (2012), 207-214.
• [13] Tunҫ, C., Instability of a nonlinear differential equation of fifth order with variable delay, Int. J. Comput. Math. Sci. 6 (2012), 73-75.
• [14] Tunҫ, C., Instability of solutions for nonlinear functional differential equations of fifth order with n-deviating arguments, Bul. Acad. Stiinte Repub. Mold. Mat. 68 (2012), no. 1, 3-14.
• [15] Tunҫ, C.; Erdogan, F., On the instability of solutions of certain non-autonomous vector differential equations of fth order, SUT J. Math. 43 (2007), no. 1, 35-48.
• [16] Tunҫ, 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.
• [17] Tunҫ, C.; Şevli, H., On the instability of solutions of certain fifth order nonlinear differential equations, Mem. Differential Equations Math. Phys. 35 (2005), 147-156.