Hartman-Wintner type criteria for half-linear second order differential equations

Zuzana Pátíková

Mathematica Bohemica (2007)

  • Volume: 132, Issue: 3, page 243-256
  • ISSN: 0862-7959

Abstract

top
We establish Hartman-Wintner type criteria for the half-linear second order differential equation r ( t ) Φ ( x ' ) ' + c ( t ) Φ ( x ) = 0 , Φ ( x ) = | x | p - 2 x , p > 1 , where this equation is viewed as a perturbation of another equation of the same form.

How to cite

top

Pátíková, Zuzana. "Hartman-Wintner type criteria for half-linear second order differential equations." Mathematica Bohemica 132.3 (2007): 243-256. <http://eudml.org/doc/250258>.

@article{Pátíková2007,
abstract = {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.},
author = {Pátíková, Zuzana},
journal = {Mathematica Bohemica},
keywords = {half-linear differential equation; Hartman-Wintner criterion; Riccati equation; principal solution; half-linear differential equation; Hartman-Wintner criterion; Riccati equation; principal solution},
language = {eng},
number = {3},
pages = {243-256},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Hartman-Wintner type criteria for half-linear second order differential equations},
url = {http://eudml.org/doc/250258},
volume = {132},
year = {2007},
}

TY - JOUR
AU - Pátíková, Zuzana
TI - Hartman-Wintner type criteria for half-linear second order differential equations
JO - Mathematica Bohemica
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 132
IS - 3
SP - 243
EP - 256
AB - 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.
LA - eng
KW - half-linear differential equation; Hartman-Wintner criterion; Riccati equation; principal solution; half-linear differential equation; Hartman-Wintner criterion; Riccati equation; principal solution
UR - http://eudml.org/doc/250258
ER -

References

top
  1. 10.1023/A:1022911815254, Georgian Math. J. 6 (1999), 401–414. (1999) MR1692963DOI10.1023/A:1022911815254
  2. 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. (2004) Zbl1090.34027MR2166491
  3. Oscillation and nonoscillation criteria for half-linear second order differential equations, (to appear). (to appear) MR2259737
  4. Hille-Wintner type comparison criteria for half-linear second order differential equations, Arch. Math., Brno 42 (2006), 185–194. (2006) MR2240356
  5. Half-Linear Differential Equations, North Holland Mathematics Studies 202, Elsevier, Amsterdam, 2005. (2005) MR2158903
  6. Regular half-linear second order differential equations, Arch. Math. 39 (2003), 233–245. (2003) MR2010724
  7. Ordinary Differential Equations, SIAM, Philadelphia, 2002. (2002) Zbl1009.34001MR1929104
  8. Principal solutions of nonoscillatory half-linear differential equations, Adv. Math. Sci. Appl. 18 (1998), 745–759. (1998) MR1657164
  9. 10.1007/BF03322512, Result. Math. 37 (2000), 56–83. (2000) MR1742294DOI10.1007/BF03322512
  10. A Picone type identity for half-linear differential equations, Acta Math. Univ. Comenianea 68 (1999), 137–151. (1999) MR1711081
  11. On oscillation and nonoscillation of a second order half-linear equation, Georgian Math. J. 2 (2000), 329–346. (2000) MR1779555
  12. 10.32917/hmj/1206127634, Hiroshima Math. J. 25 (1995), 585–594. (1995) MR1364076DOI10.32917/hmj/1206127634
  13. Analogue of the Hartman theorem, Diff. Urav. 25 (1989), 216–222. (Russian) (1989) MR0994702
  14. Asymptotic Properties of Solutions of Systems of Nonlinear Nonautonomous Ordinary Differential Equations, Masaryk University Press, Brno, 2004. (2004) Zbl1154.34300MR2144761
  15. Principal and nonprincipal solutions of a nonoscillatory system, Tbiliss. Gos. Univ. Inst. Prikl. Mat. Trudy 31 (1988), 100–117. (1988) MR1001343
  16. Half-linear Hartman-Wintner theorems, Stud. Univ. Žilina Math. Ser. 15 (2002), 56–66. (2002) Zbl1051.34026MR1980763

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.