@Article{Naito2021,
author = "Naito, Manabu",
title = "Remarks on the existence of nonoscillatory solutions of half-linear ordinary differential equations, I",
journal = "Opuscula Math.",
year = "2021",
volume = "41",
number = "1",
pages = "71--94",
doi = "https://doi.org/10.7494/OpMath.2021.41.1.71",
url = "https://doi.org/10.7494/OpMath.2021.41.1.71",
abstract = "We consider the half-linear differential equation of the form \[(p(t)|x'|^{\alpha}\mathrm{sgn} x')' + q(t)|x|^{\alpha}\mathrm{sgn} x = 0, \quad t\geq t_{0},\] under the assumption \(\int_{t_{0}}^{\infty}p(s)^{-1/\alpha}ds =\infty\). It is shown that if a certain condition is satisfied, then the above equation has a pair of nonoscillatory solutions with specific asymptotic behavior as \(t \to \infty\).",
keywords = "asymptotic behavior, nonoscillatory solution, half-linear differential equation, Hardy-type inequality",
issn = "1232-9274"
}