Hille-Wintner type comparison kriteria for half-linear second order differential equations

Ondřej Došlý; Zuzana Pátíková

Archivum Mathematicum (2006)

  • Volume: 042, Issue: 2, page 185-194
  • ISSN: 0044-8753

Abstract

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We establish Hille-Wintner type comparison 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

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Došlý, Ondřej, and Pátíková, Zuzana. "Hille-Wintner type comparison kriteria for half-linear second order differential equations." Archivum Mathematicum 042.2 (2006): 185-194. <http://eudml.org/doc/249778>.

@article{Došlý2006,
abstract = {We establish Hille-Wintner type comparison 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 = {Došlý, Ondřej, Pátíková, Zuzana},
journal = {Archivum Mathematicum},
keywords = {half-linear differential equation; Hille-Wintner comparison criterion; Riccati equation; principal solution; half-linear differential equation; Hille-Wintner comparison criterion; Riccati equation},
language = {eng},
number = {2},
pages = {185-194},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Hille-Wintner type comparison kriteria for half-linear second order differential equations},
url = {http://eudml.org/doc/249778},
volume = {042},
year = {2006},
}

TY - JOUR
AU - Došlý, Ondřej
AU - Pátíková, Zuzana
TI - Hille-Wintner type comparison kriteria for half-linear second order differential equations
JO - Archivum Mathematicum
PY - 2006
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 042
IS - 2
SP - 185
EP - 194
AB - We establish Hille-Wintner type comparison 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; Hille-Wintner comparison criterion; Riccati equation; principal solution; half-linear differential equation; Hille-Wintner comparison criterion; Riccati equation
UR - http://eudml.org/doc/249778
ER -

References

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  13. Řezníčková J., Half-linear Hartman-Wintner theorems, Stud. Univ. Žilina Math. Phys. Ser. 15 (2002), 56–66. Zbl1051.34026MR1980763
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