Author, Subjects, Keywords

Cited Author

 
 
   » By Author or Editor
 » Browse Author by Alphabet
 » By Journal
 » By Subjects
 » By Affiliations
 » By Type
 » By Year
 » By Latest Additions
 
 
   » By Author
 » Top 20 Authors
 » Top 20 Article
 » Top 20 Journal Cited
 » Top 20 Cited
 » Top 20 Author Cited
 » Usage Since Sept 2007


 
 
 

Login | Create Account

About Uniform Boundedness and Convergence of Solutions of Certain Non-Linear Differential Equations of Fifth-Order

Tunc, C., (2007) About Uniform Boundedness and Convergence of Solutions of Certain Non-Linear Differential Equations of Fifth-Order. Bulletin of the Malaysian Mathematical Sciences Society, 30 (1). pp. 1-12. ISSN 0126-6705

Full text not available from this repository.

Official URL: http://math.usm.my/bulletin/pdf/v30n1/v30n1p1.pdf

Affiliations

Yüzüncü Yil University, Faculty of Arts and Sciences, Dept. of Mathematics

Abstract

In this paper, we establish sufficient conditions under which all solutions of equation of the type $x^{(5)} + f(t,x,\dot{x}, \ddot{x},\dot{\ddot{x}},x^{(4)}) + \phi (t, \dot{x}, \ddot{x},\dot{\ddot{x}}) + \psi (t,x,\dot{x},\ddot{x})+ g(t,x, \dot{x}) + e(t)h(x) = p(t,x,\dot{x},\ddot{x},\dot{\ddot{x}},x^{(4)})$ are uniformly bounded and tend to zero as $t \rightarrow \infty$ . Our theorem is stated in a more general form; it extends some related results known in the literature. Also, the relevance of our result is to show that the results established in Abou El-Ela and Sadek [2,3] and Sadek [13] contain some superfluous conditions.

2000 Mathematics Subject Classification: 34D05.

Item Type:Journal
Keywords:Asymptotic behavior, boundedness, convergence, differential equation of fifth-order.
Subjects:Q Science, Computer Science
ID Code:1360

[1] A.M.A. Abou-El-Ela and A.I. Sadek, On the asymptotic behaviour of solutions of some differential equations of the fourth-order, Ann. Differential Equations 8(1)(1992), 1.—12.

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

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

[4] J.R. Craef, L. Hatvani, J. Karsai and P.W. Spikes, Boundedness and asymptotic behavior of solutions of second order nonlinear differential equations, Publ. Math. Debrecen 36(1—4)(1989), 85-99.

[5] T. Hara, On the asymptotic behavior of solutions of certain third order ordinary differential equations, Proc. Japan Acad. 47(1971), suppl. II, 903-908.

[6] T. Hara, On the asymptotic behavior of the solutions of some third and fourth order non-autonomous differential equations, Publ. Res. Inst. Math. Sci. 9(1973/74), 649-673.

[7] T. Hara, On the asymptotic behavior of solutions of certain non-autonomous differential equations, Osaka J. Math. 12(2)(1975), 267-282.

[8] T. Hara, On the uniform ultimate boundedness of the solutions of certain third order differential equations, J. Math. Anal. Appl. 80(2)(1981), 533-544.

[9] A. M. Lyapunov, Stability of motion, Academic Press, London, 1966, 203.

[10] M. Nakashima, Asymptotic behavior of the solutions of some third order differential equations, Rep. Fac. Sci. Kagoshima Univ. 4(1971), 7—15.

[11] C. Qian, Asymptotic behavior of a third-order nonlinear differential equation, J. Math. Anal. Appl. 284(1)(2003), 191-205.

[12] A.I. Sadek, On the asymptotic behaviour of solutions of certain fourth-order ordinary differential equations, Math. Japon. 45(3)(1997), 527—540.

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

[14] J.D. Schuur, The asymptotic behavior of a solution of the third order linear differential equation, Proc. Amer. Math. Soc. 18(1967), 391—393.

[15] Y.P. Singh, The asymptotic behavior of solutions of linear third order differential equations, Proc. Amer. Math. Soc. 20(2)(1969), 309—314.

[16] K.E. Swick, Asymptotic behavior of the solutions of certain third order differential equations, SIAM J. Appl. Math. 19(1970), 96—102.

[17] C. Tunç, On the asymptotic behaviour of solutions of some differential equations of the fourth order, Studia Univ. Babes-Bolyai Math. 39(2)(1994), 87—96.

[18] C. Thnç, On the asymptotic behaviour of solutions of certain fourth order non-autonomous differential equations, Studia Univ. Babes-Bolyai Math. 41(3)(1996), 95-105.

[19] C. Tunç, On the iniform boundedness of solutions of some non-autonomous differential equations of the fourth order (Chinese translation), Appl. Math. Mech. 20(6)(1999), 585—591; Appl. Math. Mech. (English ed.) 20(6)(1999), 622-628.

[20] Tunc, C. Boundedness and uniform boundedness results for certain non-autonomous differential equations of fourth order, Appl. Math. Mech. (English ad.) 22(11)(2001), 1273-1278; translated from Appl. Math. Mech. (English ed.) 22(11)(2001), 1147—1152.

[21] Tunc, C. On the asymptotic behaviour of solutions of certain fifth-order ordinary differential equations, Appl. Math. Comput. 24(8)(2003), 893-901.

[22] Tunc, C. On the asymptotic behaviour of solntiuns of certain non-autonomous differential equations, Appl. Math. Comput. 151(2)(2004), 363-378.

[23] Tunc, C. A result on the asymptotic behaviour of solutions of certain non-autonomous differential equations of the fifth order, Nonlinear Phenom. Complex Syst. 7(4)(2004), 359-367.

[24] Tunc, C. A study of the asymptotic behaviour of solutions of certain non-autonomous differential equations of the fifth order, Appl. Math. Gomput. 154(1)(2004), 103—113.

[25] Tunc, C. On the asymptotic behavior of solutions of certain third-order nonlinear differential equations, J. Appl. Math. Stoch. Anal. 2005(1), 29—35.

[26] Tunc, C. Uniform ultimate boundedness solutions of third-ordercnonlinear differential equations, Kuwait J. Sci. Engrg. 32(1)(2005), 39—48.

[27] M. Yamamoto, Further results for the solutions of certain third order non-autonomous differential equations, Proc. Japan. Acad. 49(1973), 317—322.

[28] T. Yoshizawa, Asymptotic behavior of solutions of a system of differential equations, Contributions to Differential Equations 1(1963), 371—387.

[29] T. Yoshizawa, Stability theory by Liapunov’s second method, The Mathematical Society of Japan, Tokyo, 1966.

[30] Y. V. Zhernovyi and V. G. Kostenko, Asymptotic behavior of the solutions of fifth-order linear ordinary differential equations, (Ukrainian) Visnik Lcprimeiv Derzh. Univ. Ser. Mekh. Mat. 18(1981), 18—21.

Repository Staff Only: item control page
 
 
 
 
 
   
© Copyright 2007 MyAIS Faculty of Computer Science and Information Technology, University of Malaya – All Rights Reserved. Malaysian Abstracting and Indexing System is powered by EPrints 3 which is developed by the School of Electronics and Computer Science at the University of Southampton. More information and software credits.