[PDF] Top 20 Oscillation criteria for second order nonlinear delay dynamic equations of neutral type

... 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

... new oscillation criteria for the second-order nonlinear delay dynamic equations on time ...the oscillation of the second-order nonlinear ... See full document

... this type arise in a number of important applications such as problems in population dynamics when maturation and gestation are included, in cobweb mod- els, in economics where demand depends on the price at an ... See full document

... where τ ∈ R and t − τ ∈ T, f : R → R is continuous and nondecreasing f u > k > 0, and ufu > 0 for u / 0, and they established the equivalence of the oscillation of 1.3 and 1.4, from which obtained some ... See full document

... of τ(t) ≤ t, assumption τ(δ(t)) < t is already satisfied when δ(t) < t and the proofs do not change. Assumption τ(t) < t implies the immediate result τ(δ(t)) < δ(t). Therefore, we conclude the following which ... See full document

... The natural question now is: Can one obtain new oscillation criteria for (.) that improve the results in [, , , , ]? The aim of this paper is to give an affirmative answer to this question. As a ... See full document

... interval oscillation criteria were recently extended to second-order dynamic equations in ...the second order nonlinear dynamic equations on ... See full document

... the oscillation constant. Other results on the oscillation constant for difference equations can be found in [–] and the references cited ... See full document

... the oscillation and nonoscillation of solutions of various equations on time scales, and we refer the reader to Bohner and Saker [5], Erbe [6], Erbe et ...the oscillation of the solutions of ... See full document

... φt, t, l 0, φt, l, l 0, and φt, s, l > 0, for l < s < t, and has the partial derivative ∂φ/∂s on E such that ∂φ/∂s is locally integrable with respect to s in E. By choosing the special function φ, it is possible ... 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

... 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

... The purpose of this paper is to obtain a new sufficient condition for oscillation of (.). The result obtained is essentially new for equations (.)-(.). This paper is organized as follows. In Section , ... See full document

... studying oscillation of solutions to different classes of differential equations due to the fact that they have numerous appli- cations in natural sciences and engineering; see, ...of ... See full document

... Candan Advances in Difference Equations 2013, 2013 112 http //www advancesindifferenceequations com/content/2013/1/112 R ES EA RCH Open Access Oscillation criteria for second order nonlinear neutral d[.] ... See full document

... Thandapani, Oscillatory and nonoscillatory behavior of second order neutral delay difference equations, Math.. Thandapani, Oscillatory and nonoscillatory behavior of second order neutral[r] ... See full document

... where the function φ will be defined in the next section. We will still assume that the functions r(t), p(t), and q(t) change sign for arbitrarily large values of t, and conditions (A), (B), and (C) are not needed. Hence, ... 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

... Philos-type oscillation criteria for second order nonlinear neutral delay dynamic equations on time scales, ...Long, Oscillation ... 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