Previous |  Up |  Next

Article

Title: Continuability, boundedness, and convergence to zero of solutions of a perturbed nonlinear ordinary differential equation (English)
Author: Graef, John R.
Author: Spikes, Paul W.
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 45
Issue: 4
Year: 1995
Pages: 663-683
.
Category: math
.
MSC: 34A34
MSC: 34C11
MSC: 34C15
MSC: 34D05
MSC: 34D10
idZBL: Zbl 0851.34050
idMR: MR1354925
DOI: 10.21136/CMJ.1995.128549
.
Date available: 2009-09-24T09:51:39Z
Last updated: 2020-07-29
Stable URL: http://hdl.handle.net/10338.dmlcz/128549
.
Reference: [1] Z. S. Athanassov: Boundedness criteria for solutions of certain second order nonlinear differential equations.J. Math. Anal. Appl. 123 (1987), 461–479. Zbl 0642.34031, MR 0883702, 10.1016/0022-247X(87)90324-6
Reference: [2] J. W. Baker: Stability properties of a second order damped and forced nonlinear differential equation.SIAM J. Appl. Math. 27 (1974), 159–166. Zbl 0289.34067, MR 0350138, 10.1137/0127013
Reference: [3] R. J. Ballieu and K. Peiffer: Attractivity of the origin for the equation $\ddot{x} + f(t,x,\dot{x})\*|\dot{x}|^{\alpha } \dot{x} + g(x) = 0$.J. Math. Anal. Appl. 65 (1978), 321–332. MR 0506309
Reference: [4] L. H. Erbe and Z. Liang: Qualitative behavior of a generalized Emden-Fowler differential system.Czech. Math. J. 41 (116) (1991), 454–466. MR 1117799
Reference: [5] S. R. Grace and B. S. Lalli: Oscillation and convergence to zero of solutions of damped second order nonlinear differential equations.J. Math. Anal. Appl. 102 (1984), 539–548. MR 0755982, 10.1016/0022-247X(84)90191-4
Reference: [6] J. R. Graef, L. Hatvani, J. Karsai, and P. W. Spikes: Boundedness and asymptotic behavior of solutions of second order nonlinear differential equations.Publ. Math. Debrecen 36 (1989), 85–99. MR 1047021
Reference: [7] J. R. Graef and P. W. Spikes: Asymptotic behavior of solutions of a second order nonlinear differential equation.J. Differential Equations 17 (1975), 461–476. MR 0361275, 10.1016/0022-0396(75)90056-X
Reference: [8] J. R. Graef and P. W. Spikes: Asymptotic properties of solutions of a second order nonlinear differential equation.Publ. Math. Debrecen 24 (1977), 39–51. MR 0454188
Reference: [9] J. R. Graef and P. W. Spikes: Boundedness and convergence to zero of solutions of a forced second-order nonlinear differential equation.J. Math. Anal. Appl. 62 (1978), 295–309. MR 0492527, 10.1016/0022-247X(78)90127-0
Reference: [10] A. Halanay: Differential Equations: Stability, Oscillations, Time Lag.Academic Press, New York, 1966. MR 0216103
Reference: [11] L. Hatvani: On the stability of the zero solution of certain second order non-linear differential equations.Acta Sci. Math. (Szeged) 32 (1971), 1–9. Zbl 0216.11704, MR 0306639
Reference: [12] L. Hatvani: On the asymptotic behavior of the solutions of $(p(t)x^{\prime })^{\prime } + q(t)f(x) = 0$.Publ. Math. Debrecen 19 (1972), 225–237. MR 0326064
Reference: [13] L. Hatvani: On the stability of the zero solution of nonlinear second order differential equations.Acta Sci. Math. (Szeged) (to appear). Zbl 0790.34046, MR 1243290
Reference: [14] J. Karsai: Attractivity theorems for second order nonlinear differential equations.Publ. Math. Debrecen 30 (1983), 303–310. Zbl 0601.34039, MR 0739492
Reference: [15] J. Karsai: Some attractivity results for second order nonlinear ordinary differential equations.in: Qualitative Theory of Differential Equations, B. Sz.-Nagy and L. Hatvani (eds.), Colloquia Mathematica Societatis János Bolyai, Vol. 53, North-Holland, Amsterdam, 1983, pp. 291–305. MR 1062654
Reference: [16] Š. Kulcsár: Boundedness, convergence and global stability of solutions of a nonlinear differential equation of the second order.Publ. Math. Debrecen 37 (1990), 193–201. MR 1082298
Reference: [17] Š. Kulcsár: Boundedness and stability of solutions of a certain nonlinear differential equation of the second order.Publ. Math. Debrecen 40 (1992), 57–70. MR 1154490
Reference: [18] A. C. Lazer: A stability condition for the differential equation $y^{\prime \prime } + p(x)y = 0$.Michigan Math. J. 12 (1965), 193–196. MR 0176168, 10.1307/mmj/1028999309
Reference: [19] K. S. Mamii and D. D. Mirzov: Properties of solutions of a second-order nonlinear differential equation on a half-axis.Differentsial’nye Uravneniya 7 (1971), 1330–1332. MR 0288349
Reference: [20] S. N. Olekhnik: The boundedness of solutions of a second-order differential equation.Differentsial’nye Uravneniya 9 (1973), 1994–1999. (Russian) Zbl 0313.34031, MR 0333345
Reference: [21] B. K. Sahoo: Asymptotic properties of solutions of a second order differential equation.Bull. Calcutta Math. Soc. 83 (1991), 209–226. Zbl 0755.34028, MR 1199402
Reference: [22] F. J. Scott: New partial asymptotic stability results for nonlinear ordinary differential equations.Pacific J. Math. 72 (1977), 523–535. Zbl 0366.34040, MR 0466793, 10.2140/pjm.1977.72.523
Reference: [23] F. J. Scott: On a partial asymptotic stability theorem of Willett and Wong.J. Math. Anal. Appl. 63 (1978), 416–420. Zbl 0383.34042, MR 0481295, 10.1016/0022-247X(78)90087-2
Reference: [24] P. W. Spikes: Some stability type results for a nonlinear differential equation.Rend. Math. (6) 9 (1976), 259–271. Zbl 0346.34034, MR 0409980
Reference: [25] N. Vornicescu: On the asymptotic behavior of the solutions of the differential equation $x^{\prime \prime } + fx = 0$.Bul. Stiint. Inst. Politehn. Cluj 14 (1971), 21–25. MR 0318608
Reference: [26] P. X. Weng: Boundedness and asymptotic behavior of solutions of a second-order functional differential equation.Ann. Differential Equations 8 (1992), 367–378. Zbl 0765.34053, MR 1192175
Reference: [27] D. Willett and J. S. W. Wong: Some properties of the solutions of $(p(t)x^{\prime })^{\prime } +q(t)f(x) = 0$.J. Math. Anal. Appl. 23 (1968), 15–24. MR 0226117
Reference: [28] J. S. W. Wong: Some stability conditions for $x^{\prime \prime } + a(t) x^{2n - 1} = 0$.SIAM J. Appl. Math. 15 (1967), 889–892. MR 0221042, 10.1137/0115077
Reference: [29] J. S. W. Wong: Remarks on stability conditions for the differential equation $x^{\prime \prime } +a(t)f(x) = 0$.J. Austral. Math. Soc. 9 (1969), 496–502. Zbl 0184.11905, MR 0241772, 10.1017/S144678870000745X
Reference: [30] E. H. Yang: Boundedness conditions for solutions of the differential equation $(a(t)x^{\prime })^{\prime } + f(t,x) = 0$.Nonlinear Anal. 8 (1984), 541–547. Zbl 0537.34030, MR 0741607, 10.1016/0362-546X(84)90092-0
.

Files

Files Size Format View
CzechMathJ_45-1995-4_6.pdf 2.041Mb application/pdf View/Open
Back to standard record
Partner of
EuDML logo