文章基本信息

标题：Oscillation of second order neutral dynamic equations with deviating arguments on time scales
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作者：Ying Sui ; Zhenlai Han
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2018
卷号：2018
期号：1
页码：337
DOI：10.1186/s13662-018-1773-x
语种：English
出版社：Hindawi Publishing Corporation
摘要：In this paper, we consider the following second order neutral dynamic equations with deviating arguments on time scales: ( r ( t ) ( z Δ ( t ) ) α ) Δ + q ( t ) f ( y ( m ( t ) ) ) = 0 , $$\bigl(r(t) \bigl(z^{\Delta}(t)\bigr)^{\alpha}\bigr)^{\Delta}+q(t)f \bigl(y\bigl(m(t)\bigr)\bigr)=0, $$ where z ( t ) = y ( t ) + p ( t ) y ( τ ( t ) ) $z(t)=y(t)+p(t)y(\tau(t))$ , m ( t ) ≤ t $m(t)\leq t$ or m ( t ) ≥ t $m(t)\geq t$ , and τ ( t ) ≤ t $\tau(t)\leq t$ . Some new oscillatory criteria are obtained by means of the inequality technique and a Riccati transformation. Our results extend and improve many well-known results for oscillation of second order dynamic equations. Some examples are given to illustrate the main results.
关键词：Time scales ; Oscillation ; Neutral ; Deviating arguments