Stability and boundedness results for solutions of certain third order nonlinear vector differential equations

Nonlinear Dynamics

Volumn 45, Issue 3-4, 2006, Pages 273-281

  Tunç, Cemil ^a   Ateş, Muzaffer ^a  

^a YUZUNCU YIL UNIVERSITY   (Turkey)

Author keywords

Boundedness; Differential equation of third order; Lyapunov function; Stability

Indexed keywords

ASYMPTOTIC STABILITY; DIFFERENTIAL EQUATIONS; FUNCTION EVALUATION; ORDINARY DIFFERENTIAL EQUATIONS; PROBLEM SOLVING; SYSTEM STABILITY; VECTORS;

BOUNDEDNESS; DIFFERENTIAL EQUATION OF THIRD ORDER; LYAPUNOV FUNCTION; NONLINEAR VECTOR DIFFERENTIAL EQUATIONS;

NONLINEAR EQUATIONS;

EID: 33746253628     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-006-1437-3     Document Type: Article

References (29)

1. Reissig, R., Sansone, G., and Conti, R., Nonlinear Differential Equations of Higher Order, Noordhoff, Groningen, 1974.
2. Ezeilo, J. O. C., 'Periodic solutions of certain third order differential equations', Atti della Accademia Nazionale dei Lincei. Rendiconti. Chase di Science Fisiche, Matematiche e Naturali. Serie 57(8), 1974, 1-2;
3. Ezeilo, J. O. C., 'Periodic solutions of certain third order differential equations', Atti della Accademia Nazionale dei Lincei. Rendiconti. Chase di Science Fisiche, Matematiche e Naturali. Serie 57(8), 1975, 54-60.
4. Ezeilo, J.O.C., 'Periodic solutions of certain third order differential equations of thenondissipative type', Attidella Accademia Nazionale dei Lincei. Rendiconti. Classe di Scienze Fisiche, Matematiche e Naturali. Serie 63(8), 1977, 3-4;
5. Ezeilo, J.O.C., 'Periodic solutions of certain third order differential equations of thenondissipative type', Attidella Accademia Nazionale dei Lincei. Rendiconti. Classe di Scienze Fisiche, Matematiche e Naturali. Serie 63(8), 1978, 212-224.
6. Feng, C. H., 'On the existence of almost periodic solutions of nonlinear third-order differential equations', Annals of Differential Equations 9(4), 1993, 420-424.
7. Feng, C. H., The existence of periodic solutions for a third-order nonlinear differential equation', (Chinese) Gongcheng Shuxue Xuebao 11(2), 1994, 113-117.
8. Mehri, B., 'Periodic solution for certain nonlinear third order differential equations', Indian Journal of Pure and Applied Mathematics 21(3), 1990, 203-210.
9. Mehri, B. and Shadman, D., 'Periodic solutions of certain third order nonlinear differential equations', Studia Scientiarum Mathematicarum Hungarica 33(4), 1997, 345-350.
10. Qian, C., 'On global stability of third-order nonlinear differential equations', Nonlinear Analysis: Theory, Methods & Applications Ser. A 42(4), 2000, 651-661.
11. Qian, C., 'Asymptotic behavior of a third-order nonlinear differential equation', Journal of Mathematical Analysis and Applications 284(1), 2003, 191-205.
12. Shadman, D. and Mehri, B., 'On the periodic solutions of certain nonlinear third order differential equations', Zeiachrift für Angewandte Mathematik und Mechanik 75(2), 1995, 164-166.
13. Tejumola, H. O., 'Periodic solutions of certain third order differential equations', Atti della Accademia Nazionale dei Lincei. Rendiconti. Classe di Scienze Fisiche, Matematiche e Naturali. Serie 66(8), 1979, no. 4, 243-249.
14. Vladimir, V., 'To exiatence of the periodic solution of a third-order nonlinear differential equation', Acta Universitatis Palackianas Olomucensis. Facultas Rerum Naturalium. Mathematica 29, 1990, 123-163.
15. Yoshizawa, T., 'Stability theory and the existence of periodic solutions', and almost periodic solutions', Applied Mathematical Sciences, Vol. 14, Springer-Verlag, New York-Heidelberg, 1975.
16. Zhang, X. Z., 'Stability in the large of a class of third-order nonlinear ordinary differential equations', Kexue Tongbao (English edn.) 28(7), 1983, 999-1000.
17. Wang, L. and Wang, M. Q., 'On the construction of globally asymptotically stable Lyapunov functions for a type of nonlinear third-order system', Acta Mathematicae Applicatae Sinica 6(3), 1983, 309-323.
18. Abou-El-Ela, A. M. A., 'Boundedness of the solutions of certain third-order vector differential equations', Annals of Differential Equations 1(2), 1985, 127-139.
19. Afuwape, A.U., 'Ultimate boundedness results for a certain system of third-order nonlinear differential equations', Journal of Mathematical Analysis and Applications 97(1), 1983, 140-150.
20. Afuwape, A. U., 'Further ultimate boundedness results for a third-order nonlinear system of differential equations', Unione Matematica Italiana Bollettino C. Serie VI 4(1), 1985, 347-361.
21. Edziwy Spolhk, S., 'Stability of certain third order vector differential equations', Bulletin de l'Académie Polonaise des Sciences. Série des Sciences Mathématiques, Astronomiques et Physiques 23, 1975, 15-21.
22. Ezeilo, J. O. C. and Tejumola, H. O., 'Boundedness and periodicity of solutions of a certain system of third-order non-linear differential equations', Annali di Matematica Pura ed Applicata 74(4), 1966, 283-316.
23. Feng, C., 'On the existence of periodic solutions for a certain system of third order nonlinear differential equations', Annals of Differential Equations 11(3), 1995, 264-269.
24. Kalantarov, V. and Tiryaki, A., 'On the stability results for third order differential-operator equations', Turkish Journal of Mathematics 21(2), 1997, 179-186.
25. Meng, F. W., 'Ultimate boundedness results for a certain system of third order nonlinear differential equations', Journal of Mathematical Analysis and Applications 177(2), 1993, 496-509.
26. Tiryaki, A., 'Boundedness and periodicity results for a certain system of third order nonlinear differential equations', Indian Journal of Pure and Applied Mathematics 30(4), 1999, 361-372.
27. Tunç, C., 'On the boundedness and periodicity of the solutions of a certain vector differential equation of third-order', Applied Mathematics and Mechanics (English edn.) 20(2), 1999, 163-170.
28. Tunç, C., 'Uniform ultimate boundedness of the solutions of third-order nonlinear differential equations', Kuwait Journal of Science & Engineering 32(1), 2005, 39-48.
29. Tunç, C., 'On the asymptotic behavior of solutions of certain third-order nonlinear differential equation', Journal of Applied Mathematics and Stochastic Analysis 2005(1), 2005, 29-35.