[PDF] Top 20 Oscillation criteria for second order nonlinear dynamic equations

... 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

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

... the oscillation of ...the oscillation of (). We obtain some oscillation criteria for () by developing a generalized Riccati substitution ... See full document

... Asymptotic Behavior of olutlons of Fourth Order Nonlinear Differential Equations, Proc.. An Oscillation Criterion for a Fourth Order Integrally Superllnear Differential Equation, Attl.[r] ... See full document

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

... the oscillation and nonoscillation of solutions of various equations on time scales, and we refer the reader to Bohner and Saker 5 , Erbe 6 , and Hassan 7 ...the oscillation of the solutions of delay ... 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

... well-known oscillation criteria in the literature, the interval oscillation criteria we have obtained provide further extensions of these to time ... See full document

... difference equations can be applied in several fields such as bifurcation analysis, population dynamics, stability theory, the dynamics of delayed network systems and ...difference equations has been ... See full document

... In , Saker et al. [] posed an open problem as follows: How to establish oscillation criteria for equation (.) when condition (.) holds? Assuming (.), Zhang et al. [, ] obtained some sufficient ... 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

... “Oscillation Criteria for Second Order Nonlinear Perturbed Differential Equations,” Jour- nal of Mathematical Analysis and Applications, ...for Second- ... See full document

... Equations of 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 ... See full document

... We have two aims in this paper. The first aim is to remove the condition (1.5) in Theorem 1.1 and to demonstrate this with an example. The second goal is to extend the technique developed by Rogovchenko and Tuncay ... 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

... criteria above are valid with ρ(t) = . Hence when ρ(t) =  and ψ (u) ≡ , Theorem ., The- orem . and Corollary . reduce to Theorem . and Theorem . and Theorem . in [], respectively. When α = , ψ ... See full document

... delay dynamic equations by Agarwal, Bohner and Saker in 2005 [1] (7) and the nonlinear delay dynamic equations by Sahiner [2] (6), some sufficient conditions for oscillation of ... See full document

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