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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.25 no.1 Antofagasta May 2006

http://dx.doi.org/10.4067/S0716-09172006000100001 

 

Proyecciones Journal of Mathematics
Vol. 25, No 1, pp. 1-18, May 2006.
Universidad Católica del Norte
Antofagasta - Chile

 

STABILITY RESULTS FOR THE SOLUTIONS OF CERTAIN NON-AUTONOMOUS DIFFERENTIAL EQUATIONS OF FIFTH -ORDER

 

CEMIL TUNC

Yuzuncu Yil University, Turkey

Correspondencia a:


Abstract

The paper is concerned with the stability of solutions of a class of general type fifth order non-autonomous differential equations (1.3) and (1.4). It is shown that under some less restrictive conditions that all solutions of (1.3) and (1.4) tend to zero as t → ∞. Our results improve that the results obtained by Sadek [9].

Keywords: Stability, differential equation of fifth order.


 

5. REFERENCES

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[2] Abou-El-ela, A.M.A; Sadek, A.I., On the asymptotic behaviour of solutions of certain non-autonomous differential equations. J:Math: Anal: Appl:237 (1 ), pp. 360-375, (1999).

[3] Abou-El-ela, A.M.A; Sadek, A.I., On the asymptotic behaviour of solutions of some nonautonomous differential equations. (Russian) Differ. Uravn. 36 (3) (2000), 415-417; translation in Differ: Equ: 36(3), pp. 466-470, (2000).

[4] Burganskaja, L.I., The stability in the large of the zero solution of certain fifth order nonlinear differential equations. (Russian) Differencial'nye Uravnenija 7, pp. 1752-1764, (1971).

[5] Chukwu, E.N., On the boundedness and stability properties of solutions of some differential equations of the fifth order. Ann.Math.Pura. Appl., (4) 106, pp. 245-258, (1975).

[6] Chukwu, E.N. On the boundedness and the stability of solutions of some differential equations of the fifth order. SIAM. J:Math.: Anal: 7 (2), pp. 176-194, (1976).

[7] Chukwu, E.N., Complete stability and boundedness of solutions of a nonlinear differential equation of fifth order. Stability of dynamical systems, theory and applications (Proc. Regional Conf., Mississippi State Univ., Mississippi State, Miss., 1975), pp. 111-118. Lecture Notes in Pure and Appl. Math., Vol. 28, Dekker, New York, (1977).

[8] Sadek, A.I., On the asymptotic behaviour of solutions of certain fifthorder ordinary differential equations. Appl. Math. Comput. 131 (1), pp. 1-13, (2002).

[9] Sadek, A.I., On the stability of the solutions of certain fifth order nonautonomous differential equations. Archivum Mathematicum (Brno) Tomus 41, pp. 93-106, (2005).

[10] Tunç, C., On the boundedness and the stability results for the solutions of certain fifth order differential equations. Istanbul Üniv. Fen Fak. Mat. Dergi. 54 (1995), pp. 151-160, (1997).

[11] Tunç, C., On the boundedness and the stability results for the solutions of certain fifth order differential equations. Ann. Differential Equations 12, no.3, pp. 259-266, (1996).

[12] Tunç, C., A study of the stability and boundedness of the solutions of nonlinear differential equations of the fifth order. Indian J. Pure Appl. Math. 33, no.4, pp. 519-529, (2002).

[13] Tunç, C., On the asymptotic behaviour of solutions of certain fifthorder ordinary differential equations. Applied Mathematics and Mechanics 24 (8), pp. 893-901, (2003).

[14] Tunç, C., A study of the asymptotic behaviour of solutions of certain non-autonomous differential equations of the fifth order. Appl. Math. Comput. 154 (1), pp. 103-113, (2004).

[15] Tunç, C., A result on the asymptotic behaviour of solutions of certain non-autonomous differential equations of the fifth order. Nonlinear Phenomena in Complex Systems, 7 (4), pp. 359-367, (2004).

[16] Yu, Y. H., Stability and boundedness of solutions to nonlinear differential equations of the fifth order. (Chinese) J. Central China Normal Univ. Natur. Sci. 24, no.3, pp. 267-273, (1990).

[17] ]Yoshizawa, T., Stability theory by Liapunov's second method. Publications of the Mathematical Society of Japan, Tokyo (1966).

Cemil Tunç
Department of Mathematics
Faculty of Arts and Sciences
Yüzüncü Yil University,
65080, Van - Turkey
Turkey
e-mail : cemtunc@yahoo.com

Received : July 2005. Accepted : October 2005

 

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