Abstract
Consider the Emden-Fowler dynamic equation
where \({p\in C_{rd}([t_0,\infty)_{\mathbb{T}},\mathbb{R}), \alpha}\) is the quotient of odd positive integers, and \({\mathbb{T}}\) denotes a time scale which is unbounded above and satisfies an additional condition (C) given below. We prove that if \({\int^\infty_{t_0}t^\alpha |p(t)|\Delta t<\infty}\) (and when α = 1 we also assume lim t→∞ tp(t)μ(t) = 0), then (0.1) has a solution x(t) with the property that
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Jia Baoguo is supported by the National Natural Science Foundation of China (No. 10971232).
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Erbe, L., Baoguo, J. & Peterson, A. On the asymptotic behavior of solutions of Emden–Fowler equations on time scales. Annali di Matematica 191, 205–217 (2012). https://doi.org/10.1007/s10231-010-0179-5
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DOI: https://doi.org/10.1007/s10231-010-0179-5