文章基本信息

标题：Asymptotic behavior of impulsive neutral delay differential equations with positive and negative coefficients of Euler form
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作者：Fangfang Jiang ; Jianhua Shen ; Zhicheng Ji 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：2018
卷号：2018
期号：1
页码：83
DOI：10.1186/s13662-018-1503-4
语种：English
出版社：Hindawi Publishing Corporation
摘要：In this paper, we are concerned with asymptotic properties of solutions for a class of neutral delay differential equations with forced term, positive and negative coefficients of Euler form, and constant impulsive jumps of the form { [ x ( t ) − C ( t ) g ( x ( τ ( t ) ) ) ] ′ + P ( t ) t f ( x ( α t ) ) − Q ( t ) t f ( x ( β t ) ) = h ( t ) , t ≥ t 0 > 0 , t ≠ t k , x ( t k + ) − x ( t k ) = α k , k ∈ Z + . $$ \textstyle\begin{cases} [x(t)-C(t)g(x(\tau(t)))]'+ \frac{P(t)}{t}f(x(\alpha t))-\frac {Q(t)}{t}f(x(\beta t))=h(t),\quad t\geq t_(>0, t\neq t_{k},\\ x(t_{k}^{+})-x(t_{k})=\alpha_{k},\quad k\in{\mathbb{Z}_{+}}. \end{cases} $$ By constructing auxiliary functions and applying the technique of considering asymptotic properties of nonoscillatory and oscillatory solutions we establish some sufficient conditions to guarantee that every solution of the system tends to zero as t → + ∞ $t\to+\infty$ .
关键词：Impulse ; Neutral differential equation ; Unbounded delay ; Positive and negative coefficients of Euler form ; Constant jump