# Conditional oscillation of half-linear differential equations with periodic coefficients

Archivum Mathematicum (2008)

• Volume: 044, Issue: 2, page 119-131
• ISSN: 0044-8753

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## Abstract

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We show that the half-linear differential equation ${\left[r\left(t\right)\Phi \left({x}^{\text{'}}\right)\right]}^{\text{'}}+\frac{s\left(t\right)}{{t}^{p}}\Phi \left(x\right)=0*$ with $\alpha$-periodic positive functions $r,s$ is conditionally oscillatory, i.e., there exists a constant $K>0$ such that () with $\frac{\gamma s\left(t\right)}{{t}^{p}}$ instead of $\frac{s\left(t\right)}{{t}^{p}}$ is oscillatory for $\gamma >K$ and nonoscillatory for $\gamma .

## How to cite

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Hasil, Petr. "Conditional oscillation of half-linear differential equations with periodic coefficients." Archivum Mathematicum 044.2 (2008): 119-131. <http://eudml.org/doc/250438>.

@article{Hasil2008,
abstract = {We show that the half-linear differential equation $\big [r(t)\Phi (x^\{\prime \})\big ]^\{\prime \} + \frac\{s(t)\}\{t^p\} \Phi (x) = 0 \ast$ with $\alpha$-periodic positive functions $r, s$ is conditionally oscillatory, i.e., there exists a constant $K>0$ such that () with $\frac\{\gamma s(t)\}\{t^p\}$ instead of $\frac\{s(t)\}\{t^p\}$ is oscillatory for $\gamma > K$ and nonoscillatory for $\gamma < K$.},
author = {Hasil, Petr},
journal = {Archivum Mathematicum},
keywords = {oscillation theory; conditional oscillation; half-linear differential equations; oscillation theory; conditional oscillation; half-linear differential equation},
language = {eng},
number = {2},
pages = {119-131},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Conditional oscillation of half-linear differential equations with periodic coefficients},
url = {http://eudml.org/doc/250438},
volume = {044},
year = {2008},
}

TY - JOUR
AU - Hasil, Petr
TI - Conditional oscillation of half-linear differential equations with periodic coefficients
JO - Archivum Mathematicum
PY - 2008
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 044
IS - 2
SP - 119
EP - 131
AB - We show that the half-linear differential equation $\big [r(t)\Phi (x^{\prime })\big ]^{\prime } + \frac{s(t)}{t^p} \Phi (x) = 0 \ast$ with $\alpha$-periodic positive functions $r, s$ is conditionally oscillatory, i.e., there exists a constant $K>0$ such that () with $\frac{\gamma s(t)}{t^p}$ instead of $\frac{s(t)}{t^p}$ is oscillatory for $\gamma > K$ and nonoscillatory for $\gamma < K$.
LA - eng
KW - oscillation theory; conditional oscillation; half-linear differential equations; oscillation theory; conditional oscillation; half-linear differential equation
UR - http://eudml.org/doc/250438
ER -

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