[PDF] Top 20 Oscillation Criteria for Second Order Nonlinear Neutral Delay Differential Equations

... An important tool in the study of oscillation is the integral averaging technique. Just as we can see, most oscillation results in 1, 3, 5, 7, 11, 12 involved the function class H. Say a function H Ht, s ... See full document

... where ∞ r –1/ γ (s) ds = ∞. Based on the comparison with first order delay equations and by employ the Riccati substitution technique, we improve and complement a number of well-known results. Some ... See full document

... differential equations done by many researchers is motivated by many application problems in physics, biology, ecology, and so ...obtaining oscillation criteria for different classes of differen- tial ... See full document

... Another widely used technique, applicable also in the above-mentioned case, involves the Riccati type transformation which has been used to reduce equation (E) to a first-order Riccati inequality. In 2006, Sun and ... See full document

... In this paper, motivated by the ideas in [], we obtain several new oscillation criteria for Equation () and its special cases by using generalized Riccati transformation and well known techniques. The ... 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

... 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

... the oscillation theory has been devoted to the os- cillatory and asymptotic properties of the third-order differential equations (see ...third-order nonlinear differential ... 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

... An important method in the study of oscillatory be- haviour for Equations (1.1)-(1.4) is the averaging tech- nique which comes from the classical results of Wintner [19] and Hartman [18]. Using the generalized ... See full document

... was given in [, Lemma ]. In fact, inequality (.) in a more or less general form was repeatedly used in the process of elimination of increasing positive solutions in (.), its generalizations or particular cases; ... 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

... Saker, Asymptotic Behavior of Solutions of a Third-Order Non-linear Dynamic Equation on Time Scales, Journal of Computational and Applied Mathematics 181, (2005) 92-102. Thandapani, O[r] ... 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

... Hindawi Publishing Corporation Advances in Difference Equations Volume 2010, Article ID 184180, 9 pages doi 10 1155/2010/184180 Research Article Oscillation of Even Order Neutral Delay Differential Eq[.] ... 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

... In what follows, we provide some background details regarding the study of oscillation of second-order differential equations which motivated our study. Oscillation criteria for ... See full document

... differential equations is of impor- tance both in theory and ...of neutral differential equations have a number of practical applications in the study of distributed networks containing lossless ... See full document

... the second order nonlinear differential equations with damping ...the oscillation of the differential equation with damping term in our paper is of more practical ...on ... 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 ...of neutral delay difference ... See full document