[PDF] Top 20 On the Oscillation of Second Order Neutral Delay Differential Equations

... 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

... A neutral delay differential equation is a differential equation in which the highest order derivative of the unknown function appears both with and without ...decades, oscillation of ... See full document

... The objective of this paper is to study oscillation of a forced second-order neutral differential equation. By using the generalized Riccati substitution and integral technique, a new sufficient ... See full document

... Remark . In this paper, we present some new oscillation criteria for the differential equation with a linear damping term (.). Our theorems can be applied to the cases where p ≥ , p ≤ , or p is an oscillatory ... 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

... third order differential equations, see for example [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23], and the references cited ... See full document

... of equations with nonnegative neutral coefficients; see, ...for equations with nonpositive neutral coefficients, there are relatively fewer results in the literature; see [3, 4, 6, 11, 14, ... See full document

... [30] S. R. Grace, J. R. Graef, S. Panigrahi and E. Tunc¸, On the oscillatory behavior of even order neutral delay dynamic equations on time scales, Electron. J. Qual. Theory Differ. Equ., vol. ... 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

... Remark . In this paper, we establish some new oscillation theorems for (.) in the case where p is finite or infinite on I. The criteria obtained extend the results in [] and improve those reported in []. ... 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 foundations of vibration theory for continuous media established in the first half of the 18th century by the two close collaborators Daniel Bernoulli and Leonard Euler have generated the investigation of linear ... See full document

... Impulsive differential equations are now recognized as an excellent source of models to simu- late processes and phenomena observed in theoritical physics, chemical technology, population dynamics, ... See full document

... differential equations have been studied by several authors, and several techniques have been proposed for obtaining oscillatory criteria for higher- and fourth-order differential ... See full document

... The paper is organized as follows. In the next section, by developing a Riccati transformation technique some sufficient conditions for oscillation of all solutions of 1.1 on time scales are established. In Section ... See full document

... neutral delay differential equation (2) is a system consisting of a differential equation together with an impulsive condition in which the second order derivative of the unknown ... 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 one of ... See full document

... differential equations has been shown. Many papers deal with the oscillation of neutral differential equations which are often en- countered in applied problems in science and technology; see, ... See full document

... By using Riccati transformation technique, we established sufficient conditions which insure that solution of class of third order neutral delay differential equation is oscillatory or tends ... See full document