Asymptotics and oscillation of nth-order nonlinear dynamic equations on time scales

Shao-Yan Zhang, Qi-Ru Wang and Qingkai Kong

Applied Mathematics and Computation, 2016, vol. 275, issue C, 324-334

Abstract: This paper is concerned with nth-order nonlinear dynamic equations on time scales of the form (r(t)Φγ(xΔn−1(t)))Δ+∑i=0kqi(t)Φαi(x(δi(t)))=0with n ≥ 2. By discussing the signs of ith-order derivatives of eventually positive solutions for i=1,…,n−1, and using the generalized Riccati technique and integral averaging technique, we derive new criteria for oscillation and asymptotic behavior of the equation. Our results extend many existing results in the literature.

Keywords: nth-order nonlinear dynamic equation; Time scales; Oscillation; Asymptotics; Generalized Riccati technique (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:275:y:2016:i:c:p:324-334

DOI: 10.1016/j.amc.2015.11.084

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