[PDF] Top 20 Oscillation criteria for even order neutral differential equations with distributed deviating arguments

... first order delay equations and technique of Riccati transformation, we obtain a two different conditions ensure oscilla- tion of solutions of this equation, which extend and improve results of ...for ... 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

... the oscillation and asymp- totic properties of various classes of differential equations; see, ...third-order neutral differential equations with distributed deviating ... See full document

... G t r , so each of the condition (2), (4), (5) and (6) has as many as l conditions. Meanwhile, the Riccati func- tion    t is not well-defined and there exist some small errors in the proof of the theorems. The ... See full document

... the oscillation of the third-order nonlinear neutral differential equations with damping and distributed ...The oscillation of the third-order damped equations is ... See full document

... In the following, we present some background details that motivate our research. Re- cently, Baculíková and Lacková [], Džurina and Hudáková [], Li et al. [, ], and Sun et al. [] established some ... See full document

... The purpose of this paper is to establish new oscillation criteria of Eq. (.) for γ > , a quotient of odd positive integers, where functions p(t) and r(t) may not be monotonic, δ(t, ξ ) may not be ... See full document

... It should be noted that condition (.) is a restrictive condition in the study of asymp- totic behavior of third-order differential equations. To solve this problem without requir- ing (.), Li et al. [] ... See full document

... dynamic equations on time scales, or mea- sure chains, and we refer the reader to the landmark paper of Hilger [] for a comprehen- sive treatment of the ...the oscillation and non-oscillation of ... See full document

... In Section 2, we present some preliminary lemmas and in Section 3, we establish some sufficient conditions which ensure that all solutions of equation (1.1) are either oscillatory or con[r] ... See full document

... article distributed under the Creative Commons Attribution License, which permits unrestricted use, dis- tribution, and reproduction in any medium, provided the original work is properly ... See full document

... the neutral term of the equation is u (θ (t)). Obviously, the neutral term is different from the previous ...impulsive neutral differential equations of the first or the second order, but, ... See full document

... of oscillation of differential equations, there are two techniques which are used to reduce the higher-order equations to the first-order Riccati equation or ...for oscillation ... See full document

... Onose, Asymptotic behavior of nonoscillatory solutions of functional differential equations of arbitrary order, J.. Onose, Nonoscillation theorems for differential equations with deviati[r] ... See full document

... Zhang, Oscillation of first order linear differential equations with deviating arguments, Differential Integral Equations, 1 (1988), 305-314.. [9] N.[r] ... See full document

... the oscillation theory of second order nonlinear equations with delay ...second order equation with first order delay equation, we obtain two different conditions to ensure ... See full document

... The results of this article are presented in a form which is essentially new and of high degree of generality. In this article, using a Riccati transformation and the inequality tech- nique, we offer some new sufficient ... See full document

... There has been a growing interest in the study of the oscillatory and asymptotic behavior of various classes of differential equations during the past decades; we refer the reader to [–] and the references cited ... See full document

... 0 < t < +∞, with the boundary conditions u(0) = A, u (0) = B, u (t) – au (t) = θ (t), – τ ≤ t ≤ 0; u (+∞) = C. We present sufficient conditions for the existence of a solution between a pair of lower and upper ... See full document

... on an above-unbounded time scale. By using a generalized Riccati transformation and integral averaging technique we study asymptotic behavior and derive some new oscillation criteria for the cases without ... See full document