文章基本信息

标题：Nonoscillation for higher-order nonlinear delay dynamic equations on time scales
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作者：Chunyan Tao ; Taixiang Sun ; Qiuli He 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：2016
卷号：2016
期号：1
页码：58
DOI：10.1186/s13662-016-0786-6
语种：English
出版社：Hindawi Publishing Corporation
摘要：In this paper, we investigate the nonoscillation of the higher-order nonlinear delay dynamic equation ( a n − 1 ( t ) ( a n − 2 ( t ) ( ⋯ ( a 1 ( t ) x Δ ( t ) ) Δ ⋯ ) Δ ) Δ ) Δ + u ( t ) g ( x ( δ ( t ) ) ) = R ( t ) for t ∈ [ t 0 , ∞ ) T , $$\begin{aligned} &\bigl(a_{n-1}(t) \bigl(a_{n-2}(t) \bigl(\cdots \bigl(a_)(t)x^{\Delta}(t)\bigr)^{\Delta}\cdots \bigr)^{\Delta}\bigr)^{\Delta}\bigr)^{\Delta} +u(t)g\bigl(x\bigl( \delta(t)\bigr)\bigr)=R(t) \\ &\quad\mbox{for } t\in [t_(, \infty)_{\mathbb{T}}, \end{aligned}$$ where T $\mathbb{T}$ is a scale with sup T = ∞ $\sup\mathbb{T}=\infty$ , t 0 ∈ T $t_(\in\mathbb{T}$ , and [ t 0 , ∞ ) T = { t ∈ T : t ≥ t 0 } $[t_(,\infty)_{\mathbb{T}}= \{t\in\mathbb{T}:t\geq t_(\}$ . We obtain some sufficient conditions for all solutions of this equation to be nonoscillatory.
关键词：nonoscillation ; dynamic equation ; time scale