文章基本信息

标题：Oscillation criteria for third-order functional half-linear dynamic equations
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作者：Taher S Hassan ; Ravi P Agarwal ; Wael W Mohammed 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2017
卷号：2017
期号：1
页码：111
DOI：10.1186/s13662-017-1164-8
语种：English
出版社：Hindawi Publishing Corporation
摘要：In this paper, we study the third-order functional dynamic equation { r 2 ( t ) ϕ α 2 ( [ r 1 ( t ) ϕ α 1 ( x Δ ( t ) ) ] Δ ) } Δ + q ( t ) ϕ α ( x ( g ( t ) ) ) = 0 , $$ \bigl\{ r_,(t)\phi_{\alpha_,} \bigl( \bigl[ r_)(t) \phi _{\alpha _)} \bigl( x^{\Delta}(t) \bigr) \bigr] ^{\Delta} \bigr) \bigr\} ^{\Delta}+q(t)\phi_{\alpha} \bigl( x\bigl(g(t)\bigr) \bigr) =0, $$ on an upper-unbounded time scale T $\mathbb{T}$ . We will extend the so-called Hille and Nehari type criteria to third-order dynamic equations on time scales. This work extends and improves some known results in the literature on third-order nonlinear dynamic equations and the results are established for a time scale T $\mathbb{T}$ without assuming certain restrictive conditions on T $\mathbb{T}$ . Some examples are given to illustrate the main results.
关键词：oscillation criteria ; third order ; dynamic equations ; time scales