[PDF] Top 20 New oscillation results for second order neutral delay dynamic equations

... obtain new oscillation criteria for (.) that improve the results in [, , , , ]? The aim of this paper is to give an affirmative answer to this ...obtained results improve those by [, ... See full document

... the oscillation theory of dynamic equations on time scales has become one of the research ...of second-order nonlinear delay dynamic equation ... See full document

... of oscillation of equations which are special cases of (E) has been based on a reduction of order and the comparison with oscillation of first-order delay differential ...the ... See full document

... Remark . We establish two classes of oscillation criteria for (.) without requiring the restrictive conditions (.). Note that these results are based on the assumption (.) and, as fairly noticed by ... See full document

... differential equations has been the subject of intensive study; we refer to the articles 1–13 ; Especially, the study of the oscillation of neutral delay differential equations is of ... See full document

... If all solutions of Eq. (1.1) are oscillatory, then Eq. (1.1) is said to be oscillatory. Before given the main results, we note that the initial value problem which consists of Eq. (1.1) and the initial function ... See full document

... interval oscillation criteria were recently extended to second-order dynamic equations in ...Further results on oscillatory and nonoscillatory behavior of the second ... See full document

... S.enel, Oscillation theorems for the second order damped nonlinear dynamic equation on time scales, Contemp. Zhang, Oscillation of second-order half-linear delay dynamic equations with d[r] ... See full document

... in order to unify continuous and discrete analysis see Hilger 1 ...this new theory; see the survey paper by Agarwal et ...in dynamic equations on time ... See full document

... powerful new tools for exploring connections between the traditionally separated fields, has been developing rapidly and has received much ...attention. Dynamic equations cannot only unify the ... See full document

... The rest of the paper is organized as follows: Sect. 2 is devoted to the main results of the paper. We present our investigations in two folds for Eqs. (1) and (2). Meanwhile, a relevant result on the existence of ... See full document

... some new oscillation criteria and gave sufficient conditions to ensure that all solutions of nonlinear neutral dynamic equation are oscillatory on a time scale T ... See full document

... of delay dynamic equations on time scales, in this paper, we consider the second-order nonlinear delay dynamic equation on time scales ... See full document

... Most oscillation results reported in the literature for neutral differential equation () and its particular cases have been obtained under the assumption () which significantly sim- plifies the ... See full document

... differential equations find numerous applications in natural science and ...of neutral delay differential equations, and we refer to the recent papers 2–23 and the references cited ... See full document

... difference equations, and dynamic equations on time scales have an enor- mous potential for applications in biology, engineering, economics, physics, neural net- works, social sciences, ...of ... See full document

... For the existence and uniqueness of solutions of the equations of the form 1.6, refer to the monograph 2 . As usual, we define a proper solution of 1.6 which is said to be oscillatory if it is neither eventually ... See full document

... On the Oscillation of Second-Order Nonlinear Neutral Delay Dynamic Equations on Time Scales Quanxin Zhang, Xia Song, Li Gao Department of Mathematics, Binzhou University, Shandong, China[r] ... See full document

... some new oscillation theorems for ...the results in [] and improve those reported in []. Similar results can be presented under the as- sumption that  < α ≤ ... See full document

... two new sufficient conditions which ensure that every solution of equations is oscillatory or converges to ...The results obtained improve and complement some known results in the ... See full document