Oscillation Criteria for Second-Order Quasilinear Neutral Delay Dynamic Equations on Time Scales. (1st March 2010)

• Record Type: Journal Article
• Authors: Sun, Yibing; Han, Zhenlai; Li, Tongxing; Zhang, Guangrong
• Other Names: N'Guerekata Gaston Mandata Academic Editor.
• Is Part Of: Advances in difference equations. Volume 2010(2010)
• Publication Date: 2010-03-01
• Subjects: Difference equations -- Periodicals; 515.625
• DOI: 10.1155/2010/512437
• Languages: English
• ISSNs: 1687-1847

Abstract

Abstract : We establish some new oscillation criteria for the second-order quasilinear neutral delay dynamic equations[ r ( t ) ( z Δ ( t ) ) γ ] Δ + q 1 ( t ) x α ( τ 1 ( t ) ) + q 2 ( t ) x β ( τ 2 ( t ) ) = 0 on a time scaleT, wherez ( t ) = x ( t ) + p ( t ) x ( τ 0 ( t ) ), 0 < α < γ < β . Our results generalize and improve some known results for oscillation of second-order nonlinear delay dynamic equations on time scales. Some examples are considered to illustrate our main results.