| Title:
|
Hartman-Wintner type criteria for half-linear second order differential equations (English) |
| Author:
|
Pátíková, Zuzana |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
132 |
| Issue:
|
3 |
| Year:
|
2007 |
| Pages:
|
243-256 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We establish Hartman-Wintner type criteria for the half-linear second order differential equation \[ \left(r(t)\Phi (x^{\prime })\right)^{\prime }+c(t)\Phi (x)=0,\quad \Phi (x)=|x|^{p-2}x,\ p>1, \] where this equation is viewed as a perturbation of another equation of the same form. (English) |
| Keyword:
|
half-linear differential equation |
| Keyword:
|
Hartman-Wintner criterion |
| Keyword:
|
Riccati equation |
| Keyword:
|
principal solution |
| MSC:
|
34C10 |
| idZBL:
|
Zbl 1174.34033 |
| idMR:
|
MR2355657 |
| DOI:
|
10.21136/MB.2007.134124 |
| . |
| Date available:
|
2009-09-24T22:31:30Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134124 |
| . |
| Reference:
|
[1] T. Chantladre, N. Kandelaki, A. Lomtatidze: Oscillation and nonoscillation criteria for a second order linear equation.Georgian Math. J. 6 (1999), 401–414. MR 1692963, 10.1023/A:1022911815254 |
| Reference:
|
[2] O. Došlý: Half-Linear Differential Equations.A. Cañada, P. Drábek, A. Fonda (eds.), Handbook of Differential Equations: Ordinary Differential Equations, Vol. I, Elsevier, Amsterdam, 2004, pp. 161–357. Zbl 1090.34027, MR 2166491 |
| Reference:
|
[3] O. Došlý, A. Lomtatidze: Oscillation and nonoscillation criteria for half-linear second order differential equations.(to appear). MR 2259737 |
| Reference:
|
[4] O. Došlý, Z. Pátíková: Hille-Wintner type comparison criteria for half-linear second order differential equations.Arch. Math., Brno 42 (2006), 185–194. MR 2240356 |
| Reference:
|
[5] O. Došlý, P. Řehák: Half-Linear Differential Equations.North Holland Mathematics Studies 202, Elsevier, Amsterdam, 2005. MR 2158903 |
| Reference:
|
[6] O. Došlý, J. Řezníčková: Regular half-linear second order differential equations.Arch. Math. 39 (2003), 233–245. MR 2010724 |
| Reference:
|
[7] P. Hartman: Ordinary Differential Equations.SIAM, Philadelphia, 2002. Zbl 1009.34001, MR 1929104 |
| Reference:
|
[8] Á. Elbert, T. Kusano: Principal solutions of nonoscillatory half-linear differential equations.Adv. Math. Sci. Appl. 18 (1998), 745–759. MR 1657164 |
| Reference:
|
[9] Á. Elbert, A. Schneider: Perturbations of the half-linear Euler differential equation.Result. Math. 37 (2000), 56–83. MR 1742294, 10.1007/BF03322512 |
| Reference:
|
[10] J. Jaroš, T. Kusano: A Picone type identity for half-linear differential equations.Acta Math. Univ. Comenianea 68 (1999), 137–151. MR 1711081 |
| Reference:
|
[11] N. Kandelaki, A. Lomtatidze, D. Ugulava: On oscillation and nonoscillation of a second order half-linear equation.Georgian Math. J. 2 (2000), 329–346. MR 1779555 |
| Reference:
|
[12] H. J. Li, C. C. Yeh: Oscillations of half-linear second order differential equations.Hiroshima Math. J. 25 (1995), 585–594. MR 1364076, 10.32917/hmj/1206127634 |
| Reference:
|
[13] J. D. Mirzov: Analogue of the Hartman theorem.Diff. Urav. 25 (1989), 216–222. (Russian) MR 0994702 |
| Reference:
|
[14] J. D. Mirzov: Asymptotic Properties of Solutions of Systems of Nonlinear Nonautonomous Ordinary Differential Equations.Masaryk University Press, Brno, 2004. Zbl 1154.34300, MR 2144761 |
| Reference:
|
[15] J. D. Mirzov: Principal and nonprincipal solutions of a nonoscillatory system.Tbiliss. Gos. Univ. Inst. Prikl. Mat. Trudy 31 (1988), 100–117. MR 1001343 |
| Reference:
|
[16] J. Řezníčková: Half-linear Hartman-Wintner theorems.Stud. Univ. Žilina Math. Ser. 15 (2002), 56–66. Zbl 1051.34026, MR 1980763 |
| . |
