Oscillation for Second-Order Nonlinear Delay Dynamic Equations on Time Scales

By means of Riccati transformation technique, we establish some new oscillation criteria for the second-order nonlinear delay dynamic equations on a time scale ; here is a quotient of odd positive integers with and real-valued positive rd-continuous functions defined on . Our results not only extend some results established by Hassan in 2008 but also unify the oscillation of the second-order nonlinear delay differential equation and the second-order nonlinear delay difference equation.

[1]  S. Hilger.  Analysis on Measure Chains — A Unified Approach to Continuous and Discrete Calculus , 1990 .

[2]  Samir H. Saker,et al.  Oscillation criteria for second-order nonlinear delay dynamic equations , 2007 .

[3]  A. Peterson,et al.  Dynamic Equations on Time Scales: An Introduction with Applications , 2001 .

[4]  Lynn Erbe,et al.  Oscillation Results for Second-order Linear Equations on a Time Scale , 2002 .

[5]  A. Peterson,et al.  Dynamic Equations on Time Scales , 2001 .

[6]  Y. Sahiner,et al.  Oscillation of second-order neutral delay and mixed-type dynamic equations on time scales , 2006 .

[7]  Taher S. Hassan,et al.  Oscillation criteria for half-linear dynamic equations on time scales , 2008 .

[8]  Martin Bohner,et al.  Iterated Oscillation Criteria for Delay Dynamic Equations of First Order , 2008 .

[9]  Lei Wang,et al.  Oscillation of second-order nonlinear delay dynamic equations on time scales , 2011, Comput. Math. Appl..

[10]  Zhenlai Han,et al.  Oscillation criteria for a class of second-order Emden–Fowler delay dynamic equations on time scales☆ , 2007 .

[11]  Oscillation Criteria for Second-Order Delay Dynamic Equations on Time Scales , 2007 .

[12]  Ravi P. Agarwal,et al.  Oscillation of Second Order Delay Dynamic Equations , 2005 .

[13]  Samir H. Saker,et al.  Oscillation Criteria for Second‐Order Nonlinear Dynamic Equations On Time Scales , 2003 .

[14]  Ravi P. Agarwal,et al.  Dynamic equations on time scales: a survey , 2002 .

[15]  Y. Şahı˙ner,et al.  Oscillation of second-order delay differential equations on time scales , 2005 .

[16]  Martin Bohner,et al.  Oscillation of Second Order Nonlinear Dynamic Equations on Time Scales , 2004 .