Previous |  Up |  Next

Article

Title: Hartman-Wintner type criteria for half-linear second order differential equations (English)
Author: Pátíková, Zuzana
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959
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
.
Date available: 2009-09-24T22:31:30Z
Last updated: 2012-06-18
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
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
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
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
.

Files

Files Size Format View
MathBohem_132-2007-3_3.pdf 240.8Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo