Stability results for the solutions of certain non-autonomous differential equations of fifth -order
DOI:
https://doi.org/10.4067/S0716-09172006000100001Keywords:
Stability, differential equation of fifth order, estabilidad, ecuaciones diferenciales de quinto orden.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].References
[1] Abou-El-ela, A.M.A; Sadek, A.I., A stability result for the solutions of certain fifth-order differential equations. Bull. Fac. Sci. Assiut Univ. C 24 (1), pp. 1-11, (1995).
[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 Univ. 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).
[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 Univ. 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).
Published
2017-05-08
How to Cite
[1]
C. Tunç, “Stability results for the solutions of certain non-autonomous differential equations of fifth -order”, Proyecciones (Antofagasta, On line), vol. 25, no. 1, pp. 1-18, May 2017.
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