Oscillation of Two-Dimensional Neutral Delay Dynamic Systems. (31st March 2013)

• Record Type: Journal Article
• Authors: Zhang, Xinli; Zhu, Shanliang
• Other Names: Li Changpin Academic Editor.
• Is Part Of: Advances in mathematical physics. Volume 2013(2013)
• Publication Date: 2013-03-31
• Subjects: Mathematical physics -- Periodicals; Mathematical physics; Periodicals; 530.15
• DOI: 10.1155/2013/871961
• Languages: English
• ISSNs: 1687-9120

Abstract

Abstract : We consider a class of nonlinear two-dimensional dynamic systems of the neutral type( x ( t ) - a ( t ) x ( τ 1 ( t ) ) ) Δ = p ( t ) f 1 ( y ( t ) ), y Δ ( t ) = - q ( t ) f 2 ( x ( τ 2 ( t ) ) ) . We obtain sufficient conditions for all solutions of the system to be oscillatory. Our oscillation results whena ( 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 wheref ( u ) = u . Also, as a special case when𝕋 = ℝ, our results do not requirea n to be a positive real sequence. Some examples are given to illustrate the main results.