文章基本信息

标题：Existence of the nonoscillatory solutions of higher order neutral dynamic equations on time scales
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作者：Chunyan Tao ; Taixiang Sun ; Hongjian Xi 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：2015
卷号：2015
期号：1
页码：279
DOI：10.1186/s13662-015-0621-5
语种：English
出版社：Hindawi Publishing Corporation
摘要：In this paper, we investigate the existence of the nonoscillatory solutions of the following higher order neutral dynamic equation: { r n ( t ) [ ( r n − 1 ( t ) ( ⋯ ( r 1 ( t ) ( x ( t ) − q ( t ) x ( τ ( t ) ) ) Δ ) Δ ⋯ ) Δ ) Δ ] γ } Δ + f ( t , x ( δ ( t ) ) ) = 0 $\{r_{n}(t)[(r_{n-1}(t)(\cdots(r_)(t)(x(t)-q(t)x(\tau(t)))^{\Delta })^{\Delta}\cdots)^{\Delta})^{\Delta}]^{\gamma}\}^{\Delta} +f(t,x(\delta (t)))=0$ for t ∈ [ t 0 , ∞ ) T $t\in \left .[t_(,\infty) \right ._{\mathbb{T}}$ , and obtain some necessary and sufficient conditions for the existence of nonoscillatory bounded solutions for this equation.
关键词：nonoscillatory solution ; dynamic equation ; time scale