¹ Department of Mathematics and Physics, Hebei Institute of Architecture and Civil Engineering, Zhangjiakou, China
² Information Science and Engineering College, Hebei North University, Zhangjiakou, China
³ Department of Mechanic and Engineering, Zhangjiakou Vocational Technology Institute, Zhangjiakou, China

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Abstract—To investigate the oscillatory and asymptotic behavior for a certain class of second order nonlinear neutral perturbed dynamic equations on time scales. By employing the time scales theory and some necessary analytic techniques, and introducing the class of parameter functions and generalized Riccati transformation, some new sufficient conditions for oscillation of such dynamic equations on time scales were established. The results not only improve and extend some known results in the literature, but also unify the oscillation of second order nonlinear neutral perturbed differential equations and second order nonlinear neutral perturbed difference equations. In particular, the results are essentially new under the relaxed conditions for the parameter function. Some examples are given to illustrate the main results. Dynamic equations on time scales are widely used in many fields such as computer, electrical engineering, population dynamics, and neural network, etc.

Index Terms—oscillation, nonlinear neutral perturbed dynamic equation, time scales, Riccati transformation.

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Cite: Xiuping Yu, Hua Du, and Hongyu Yang, " Oscillation Criteria for Second Order Nonlinear Neutral Perturbed Dynamic Equations on Time Scales," Journal of Computers vol. 8, no. 6, pp. 1528-1535, 2013.