| Title:
|
Global monotonicity and oscillation for second order differential equation (English) |
| Author:
|
Bartušek, M. |
| Author:
|
Cecchi, M. |
| Author:
|
Došlá, Z. |
| Author:
|
Marini, M. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
55 |
| Issue:
|
1 |
| Year:
|
2005 |
| Pages:
|
209-222 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Oscillatory properties of the second order nonlinear equation \[ (r(t)x^{\prime })^{\prime }+q(t)f(x)=0 \] are investigated. In particular, criteria for the existence of at least one oscillatory solution and for the global monotonicity properties of nonoscillatory solutions are established. The possible coexistence of oscillatory and nonoscillatory solutions is studied too. (English) |
| Keyword:
|
second order nonlinear differential equation |
| Keyword:
|
oscillatory solution |
| Keyword:
|
nonoscillatory solution |
| Keyword:
|
coexistence problem |
| MSC:
|
34C10 |
| MSC:
|
34C11 |
| idZBL:
|
Zbl 1081.34029 |
| idMR:
|
MR2121668 |
| . |
| Date available:
|
2009-09-24T11:22:20Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127971 |
| . |
| Reference:
|
[1] M. Cecchi, M. Marini and G. Villari: On some classes of continuable solutions of a nonlinear differential equation.J. Diff. Equat. 118 (1995), 403–419. MR 1330834, 10.1006/jdeq.1995.1079 |
| Reference:
|
[2] C. V. Coffman and J. S. W. Wong: On a second order nonlinear oscillation problem.Trans. Amer. Math. Soc. 147 (1970), 357–366. MR 0257473, 10.1090/S0002-9947-1970-0257473-2 |
| Reference:
|
[3] C. V. Coffman and J. S. W. Wong: Oscillation and nonoscillation theorems for second order differential equations.Funkcialaj Ekvacioj 15 (1972), 119–130. MR 0333337 |
| Reference:
|
[4] C. V. Coffman and J. S. W. Wong: Oscillation and nonoscillation of solutions of generalized Emden-Fowler equations.Trans. Amer. Math. Soc. 167 (1972), 399–434. MR 0296413, 10.1090/S0002-9947-1972-0296413-9 |
| Reference:
|
[5] L. H. Erbe and J. S. Muldowney: On the existence of oscillatory solutions to nonlinear differential equations.Ann. Mat. Pura Appl. 59 (1976), 23–37. MR 0481254 |
| Reference:
|
[6] L. H. Erbe and H. Lu: Nonoscillation theorems for second order nonlinear differential equations.Funkcialaj Ekvacioj 33 (1990), 227–244. MR 1078128 |
| Reference:
|
[7] L. H. Erbe: Nonoscillation criteria for second order nonlinear differential equations.J. Math. Anal. Appl. 108 (1985), 515–527. Zbl 0579.34027, MR 0793663, 10.1016/0022-247X(85)90042-3 |
| Reference:
|
[8] J. W. Heidel and I. T. Kiguradze: Oscillatory solutions for a generalized sublinear second order differential equation.Proc. Amer. Math. Soc. 38 (1973), 80–82. MR 0310339, 10.1090/S0002-9939-1973-0310339-X |
| Reference:
|
[9] D. V. Izjumova: On oscillation and nonoscillation conditions for solutions of nonlinear second order differential equations.Diff. Urav. 11 (1966), 1572–1586. (Russian) |
| Reference:
|
[10] M. Jasný: On the existence of oscillatory solutions of the second order nonlinear differential equation $y^{\prime \prime }+f(x)y^{2n-1}=0$.Čas. Pěst. Mat. 85 (1960), 78–83. (Russian) |
| Reference:
|
[11] I. Kiguradze and A. Chanturia: Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations.Kluwer Acad. Publ., , 1993. MR 1220223 |
| Reference:
|
[12] J. Kurzweil: A note on oscillatory solutions of the equation $y^{\prime \prime }+f(x)y^{2n-1}=0$.Čas. Pěst. Mat. 82 (1957), 218–226. (Russian) |
| Reference:
|
[13] Chiou Kuo-Liang: The existence of oscillatory solutions for the equation ${\mathrm d}^2y/{\mathrm d}t^2 +q(t)y^{r}=0$, $0<r<1$.Proc. Amer. Math. Soc. 35 (1972), 120–122. MR 0301292, 10.1090/S0002-9939-1972-0301292-2 |
| Reference:
|
[14] S. Matucci: On asymptotic decaying solutions for a class of second order differential equations.Arch. Math. (Brno) 35 (1999), 275–284. Zbl 1048.34088, MR 1725843 |
| Reference:
|
[15] J. D. Mirzov: Asymptotic properties of solutions of the systems of nonlinear nonautonomous ordinary differential equations.(1993), Adygeja Publ., Maikop. (Russian) |
| Reference:
|
[16] R. A. Moore and Z. Nehari: Nonoscillation theorems for a class of nonlinear differential equations.Trans. Amer. Math. Soc. 93 (1959), 30–52. MR 0111897, 10.1090/S0002-9947-1959-0111897-8 |
| Reference:
|
[17] J. Sugie and K. Kita: Oscillation criteria for second order nonlinear differential equations of Euler type.J. Math. Anal. Appl. 253 (2001), 414–439. MR 1808146, 10.1006/jmaa.2000.7149 |
| Reference:
|
[18] J. S. W. Wong: On the generalized Emden-Fowler equation.SIAM Rev. 17 (1975), 339–360. Zbl 0295.34026, MR 0367368, 10.1137/1017036 |
| . |
