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Asymptotic behaviors of higher order nonlinear dynamic equations on time scales

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Abstract

In this paper, we study asymptotic behaviour of solutions of the following higher order nonlinear dynamic equations

$$y^{\triangle^n}(t)+\delta p(t)f(y(g(t)))=0$$

and

$$y^{\triangle^n}(t)+\delta p(t)f(y(h(t)))=0$$

on an arbitrary time scale \(\mathbb{T}\) with \(\sup {\mathbb{T}}=\infty\), where n is a positive integer and δ=1 or −1. We obtain some sufficient conditions for the equivalence of the oscillation of the above equations.

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Authors and Affiliations

  1. College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi, 530004, P.R. China

    Taixiang Sun & Weiyong Yu

  2. Department of Mathematics, Guangxi College of Finance and Economics, Nanning, Guangxi, 530003, P.R. China

    Hongjian Xi

Authors
  1. Taixiang Sun
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  2. Hongjian Xi
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  3. Weiyong Yu
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Correspondence to Taixiang Sun.

Additional information

Project supported by NSF of China (10861002) and NSF of Guangxi (2010GXNSFA013106, 2011GXNSFA014781) and SF of Education Department of Guangxi (200911MS212).

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Sun, T., Xi, H. & Yu, W. Asymptotic behaviors of higher order nonlinear dynamic equations on time scales. J. Appl. Math. Comput. 37, 177–192 (2011). https://doi.org/10.1007/s12190-010-0428-1

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  • DOI: https://doi.org/10.1007/s12190-010-0428-1

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