Warianty tytułu
Języki publikacji
Abstrakty
We study the asymptotic behavior of solutions to a nonlinear differential equation of the second order whose coefficient of nonlinearity is a bounded function for arbitrarily large values of x in R. We obtain certain sufficient conditions which guarantee boundedness of solutions, their convergence to zero as x→∞ and their unboundedness
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
1--8
Opis fizyczny
Bibliogr. 21 poz.
Twórcy
autor
- Department of Mathemacs, Faculty of Sciences, Yüzüncü Yıl University, cemtunc@yahoo.com
autor
- Department of Primary School-Mathemacs, Faculty of Educaon, Siirt University, timurayhan@mynet.com
Bibliografia
- [1] A. Ademola and P. Arawomo, Stability, boundedness and asymptotic behaviour of solutions of certain nonlinear differential equation, Kragujevac J. Math. 35 (2010), no. 3, 431–445.
- [2] A. Bucur, About asymptotic behaviour of solutions of differential equations as x→∞ ., Gen. Math. 14 (2006), no. 2, 55–58.
- [3] A. Constantin, A note on a second order nonlinear differential system, Glasg. Math. J. 42 (2000), no. 2, 195–199.
- [4] J. O. C. Ezeilo, A note on the convergence of solutions of certain second order differential equations, Portugal. Math. 24 (1965), 49–58.
- [5] I. Kiguradze, The asymptotic behaviour of the solutions of a non linear differential equation of Emden -Fowler type, Izv. Akad. Nauk SSSR Ser. Mat. 29 (1965), no. 5, 965–986.
- [6] T. Kusano, M. Naito, and H. Usami, Asymptotic behavior of solutions of a class of second order nonlinear differential equations, Hiroshima Math. J. 16 (1986), no. 1, 149–159.
- [7] O. Lipovan, On the asymptotic behaviour of the solutions to a class of second order nonlinear differential equations, Glasgow Math. J. 45 (2003), 179–187.
- [8] A.B. Mingareilli and K. Sadarangani, Asymptotic solutions of forced nonlinear second order differential equations and their extensions, Electron. J. Differential Equations 40 (2007), pp. 40.
- [9] O. Mustafa, On the existence of solutions with prescribed asymptotic behaviour for perturbed nonlinear differential equations of second order, Glasgow Math. J. 47 (2005), 177–18.
- [10] S. Saker, Boundedness of solutions second-order forced nonlinear dynamics equation, Rocky Mountain J. Math. 36 (2006), no. 6, 2027–2039.
- [11] J. Tong, The asymptotic behaviour of a class of nonlinear differential equations of second order, Proc. Amer. Math. Soc. 84 (1982), no. 2, 235–236.
- [12] W. Trench, Asymptotic integration of linear differential equations subject to integral smallness conditions involving ordinary convergence, SIAM J. Math. Anal. 7 (1976), 213–221.
- [13] C. Tunç, Some new stability and boundedness results on the solutions of the nonlinear vector differential equations of second order, Iran. J. Sci. Technol. Trans. A Sci. 30 (2006), no. 2, 213–221.
- [14] C. Tunç, A new boundedness theorem for a class of second order differential equations, Arab. J. Sci. Eng. Sect. A Sci. 33 (2008), no. 1, 83–92.
- [15] C. Tunç, A note on boundedness of solutions to a class of non-autonomous differential equations of second order, Appl. Anal. Discrete Math. 4 (2010), 361–372.
- [16] C. Tunç, Boundedness results for solutions of certain nonlinear differential equations of second order, J. Indones. Math. Soc. 16 (2010), no. no.2, 115–127.
- [17] C. Tunç, Stability and boundedness of solutions of non-autonomous differential equations of second order, J. Comput. Anal. Appl. 13 (2011), no. 6, 1067–1074.
- [18] C. Tunç and E. Tunç, On the asymptotic behavior of solutions of certain second-order differential equations, J. Franklin Inst. 344 (2007), no. 5, 391–398.
- [19] P. Waltman, On the asymptotic behaviour of solutions of a nonlinear equation, Proc. Amer. Math. Soc. 15 (1964), 918–923.
- [20] J. Wong, Oscillation Theorems for second order nonlinear differentialequations, Bull. Inst. Math. Acad. Simca. 3 (1975), 283–309.
- [21] M. N. Qarawani, Boundedness and asymptotic behaviour of solutions of a second order nonlinear differential equation, J. Math. Res. 4 (2012), no. 3, 121–127.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.baztech-39735d35-b515-4db8-9e8f-88f486bd937f