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Asymptotic behavior of nonoscillatory solutions of half-linear ordinary differential equations

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Abstract

This paper deals with the asymptotic behavior of solutions of the half-linear differential equation

$$\begin{aligned} (p(t)|x'|^{\alpha }\mathrm {sgn}\,x')' + q(t)|x|^{\alpha }\mathrm {sgn}\,x = 0, \quad t \ge t_{0}. \end{aligned}$$

It will be shown that, for any solution x(t) of this equation, there are only two types of asymptotic behavior as \(t\rightarrow \infty \).

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  1. Department of Mathematics, Faculty of Science, Ehime University, Matsuyama, 790-8577, Japan

    Manabu Naito

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  1. Manabu Naito
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Correspondence to Manabu Naito.

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Naito, M. Asymptotic behavior of nonoscillatory solutions of half-linear ordinary differential equations. Arch. Math. 116, 559–570 (2021). https://doi.org/10.1007/s00013-020-01573-x

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  • DOI: https://doi.org/10.1007/s00013-020-01573-x

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