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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2013-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2013/871961 |
| 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. |
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| ISSN: | 1687-9120 1687-9139 |