文章基本信息

标题：The Kamenev type interval oscillation criteria of mixed nonlinear impulsive differential equations under variable delay effects
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作者：Xiaoliang Zhou ; Changdong Liu ; Ruyun Chen 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：2019
卷号：2019
期号：1
页码：1-15
DOI：10.1186/s13662-018-1931-1
出版社：Hindawi Publishing Corporation
摘要：In this paper, a class of mixed nonlinear impulsive differential equations is studied. When the delay σ ( t ) $\sigma(t)$ is variable, each given interval is divided into two parts on which the quotients of x ( t − σ ( t ) ) $x(t-\sigma(t))$ and x ( t ) $x(t)$ are estimated. Then, by introducing binary auxiliary functions and using the Riccati transformation, several Kamenev type interval oscillation criteria are established. The well-known results obtained by Liu and Xu (Appl. Math. Comput. 215:283–291, 2009) for σ ( t ) = 0 $\sigma(t)=0$ and by Guo et al. (Abstr. Appl. Anal. 2012:351709, 2012) for σ ( t ) = σ 0 $\sigma(t)=\sigma_($ ( σ 0 ≥ 0 $\sigma_(\geq0$ ) are developed. Moreover, an example illustrating the effectiveness and non-emptiness of our results is also given.
关键词：Interval oscillation ; Impulsive differential equation ; Variable delay ; Interval delay function