@Article{Naito2023,
author = "Naito, Manabu",
title = "Existence and asymptotic behavior of nonoscillatory solutions of half-linear ordinary differential equations",
journal = "Opuscula Math.",
year = "2023",
volume = "43",
number = "2",
pages = "221--246",
doi = "https://doi.org/10.7494/OpMath.2023.43.2.221",
url = "https://doi.org/10.7494/OpMath.2023.43.2.221",
abstract = "We consider the half-linear differential equation \[(|x'|^{\alpha}\mathrm{sgn}\,x')' + q(t)|x|^{\alpha}\mathrm{sgn}\,x = 0, \quad t \geq t_{0},\] under the condition \[\lim_{t\to\infty}t^{\alpha}\int_{t}^{\infty}q(s)ds = \frac{\alpha^{\alpha}}{(\alpha+1)^{\alpha+1}}.\] It is shown that if certain additional conditions are 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",
issn = "1232-9274"
}