De la Vallée Poussin type inequality and eigenvalue problem for generalized half-linear differential equation

Libor Báňa; Ondřej Došlý

Archivum Mathematicum (2014)

  • Volume: 050, Issue: 4, page 193-203
  • ISSN: 0044-8753

Abstract

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We study the generalized half-linear second order differential equation via the associated Riccati type differential equation and Prüfer transformation. We establish a de la Vallée Poussin type inequality for the distance of consecutive zeros of a nontrivial solution and this result we apply to the “classical” half-linear differential equation regarded as a perturbation of the half-linear Euler differential equation with the so-called critical oscillation constant. In the second part of the paper we study a Dirichlet eigenvalue problem associated with the investigated half-linear equation.

How to cite

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Báňa, Libor, and Došlý, Ondřej. "De la Vallée Poussin type inequality and eigenvalue problem for generalized half-linear differential equation." Archivum Mathematicum 050.4 (2014): 193-203. <http://eudml.org/doc/262117>.

@article{Báňa2014,
abstract = {We study the generalized half-linear second order differential equation via the associated Riccati type differential equation and Prüfer transformation. We establish a de la Vallée Poussin type inequality for the distance of consecutive zeros of a nontrivial solution and this result we apply to the “classical” half-linear differential equation regarded as a perturbation of the half-linear Euler differential equation with the so-called critical oscillation constant. In the second part of the paper we study a Dirichlet eigenvalue problem associated with the investigated half-linear equation.},
author = {Báňa, Libor, Došlý, Ondřej},
journal = {Archivum Mathematicum},
keywords = {generalized half-linear differential equation; de la Vallée Poussin inequality; half-linear Euler differential equation; Dirichlet eigenvalue problem; generalized half-linear differential equation; de la Vallée Poussin inequality; half-linear Euler differential equation; Dirichlet eigenvalue problem},
language = {eng},
number = {4},
pages = {193-203},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {De la Vallée Poussin type inequality and eigenvalue problem for generalized half-linear differential equation},
url = {http://eudml.org/doc/262117},
volume = {050},
year = {2014},
}

TY - JOUR
AU - Báňa, Libor
AU - Došlý, Ondřej
TI - De la Vallée Poussin type inequality and eigenvalue problem for generalized half-linear differential equation
JO - Archivum Mathematicum
PY - 2014
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 050
IS - 4
SP - 193
EP - 203
AB - We study the generalized half-linear second order differential equation via the associated Riccati type differential equation and Prüfer transformation. We establish a de la Vallée Poussin type inequality for the distance of consecutive zeros of a nontrivial solution and this result we apply to the “classical” half-linear differential equation regarded as a perturbation of the half-linear Euler differential equation with the so-called critical oscillation constant. In the second part of the paper we study a Dirichlet eigenvalue problem associated with the investigated half-linear equation.
LA - eng
KW - generalized half-linear differential equation; de la Vallée Poussin inequality; half-linear Euler differential equation; Dirichlet eigenvalue problem; generalized half-linear differential equation; de la Vallée Poussin inequality; half-linear Euler differential equation; Dirichlet eigenvalue problem
UR - http://eudml.org/doc/262117
ER -

References

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