Oscillation of Two-Dimensional Neutral Delay Dynamic Systems

We consider a class of nonlinear two-dimensional dynamic systems of the neutral type (x(t)-a(t)x(τ1(t)))Δ=p(t)f1(y(t)), yΔ(t)=-q(t)f2(x(τ2(t))). We obtain sufficient conditions for all solutions of the system to be oscillatory. Our oscillation results when a(t)=0 improve the oscillation results for...

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Bibliographic Details
Published inAdvances in Mathematical Physics Vol. 2013; pp. 555 - 561
Main Authors Zhang, Xinli, Zhu, Shanliang
Format Journal Article
LanguageEnglish
Published Hindawi Limiteds 01.01.2013
Hindawi Publishing Corporation
John Wiley & Sons, Inc
Hindawi Limited
Subjects
Delay equations
Differential equations
Differential equations, Nonlinear
Dynamical systems
Mathematical research
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Summary:We consider a class of nonlinear two-dimensional dynamic systems of the neutral type (x(t)-a(t)x(τ1(t)))Δ=p(t)f1(y(t)), yΔ(t)=-q(t)f2(x(τ2(t))). We obtain sufficient conditions for all solutions of the system to be oscillatory. Our oscillation results when a(t)=0 improve the oscillation results for dynamic systems on time scales that have been established by Fu and Lin (2010), since our results do not restrict to the case where f(u)=u. Also, as a special case when 𝕋=ℝ, our results do not require an to be a positive real sequence. Some examples are given to illustrate the main results.
ISSN:1687-9120
1687-9139
DOI:10.1155/2013/871961