文章基本信息

标题：Semi-nonoscillation intervals in the analysis of sign constancy of Green’s functions of Dirichlet, Neumann and focal impulsive problems
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作者：Alexander Domoshnitsky ; Guy Landsman
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2017
卷号：2017
期号：1
页码：81
DOI：10.1186/s13662-017-1134-1
语种：English
出版社：Hindawi Publishing Corporation
摘要：We consider the following second order differential equation with delay: { ( L x ) ( t ) ≡ x ″ ( t ) + ∑ j = 1 p a j ( t ) x ′ ( t − τ j ( t ) ) + ∑ j = 1 p b j ( t ) x ( t − θ j ( t ) ) = f ( t ) , t ∈ [ 0 , ω ] , x ( t k ) = γ k x ( t k − 0 ) , x ′ ( t k ) = δ k x ′ ( t k − 0 ) , k = 1 , 2 , … , r . $$\textstyle\begin{cases} (Lx)(t)\equiv{x''(t)+\sum_{j=1}^{p} {a_{j}(t)x'(t-\tau_{j}(t))}+\sum_{j=1}^{p} {b_{j}(t)x(t-\theta_{j}(t))}}=f(t), & t\in[0,\omega], \\ x(t_{k})=\gamma_{k}x(t_{k}-0), x'(t_{k})=\delta_{k}x'(t_{k}-0), & k=1,2,\ldots,r. \end{cases} $$ In this paper we use focal problems to analyze the sign constancy of Green’s functions.
关键词：impulsive equations ; Green’s functions ; positivity/negativity of Green’s functions ; boundary value problem ; second order