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 $\gamma < K$.
@article{116929,
author = {Petr Hasil},
title = {Conditional oscillation of half-linear differential equations with periodic coefficients},
journal = {Archivum Mathematicum},
volume = {044},
year = {2008},
pages = {119-131},
zbl = {1212.34110},
mrnumber = {2432849},
language = {en},
url = {http://dml.mathdoc.fr/item/116929}
}
Hasil, Petr. Conditional oscillation of half-linear differential equations with periodic coefficients. Archivum Mathematicum, Tome 044 (2008) pp. 119-131. http://gdmltest.u-ga.fr/item/116929/
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