[PDF] Top 20 Oscillation of Second Order Mixed Nonlinear Delay Dynamic Equations

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

... concerning oscillation and nonoscillation of solutions to neutral differential and dynamic equations on time scales, we refer the reader to [, ] and [–], and the references cited ...a ... See full document

... Erbe and Peterson [] also discussed the oscillation of (), where r(t) > . When no ex- plicit sign assumptions are made with respect to the coefficient p, they established some sufficient conditions for the ... See full document

... the delay argument τ plays an important role in oscillation of second-order neutral delay dynamic equations; see the details in Example ... See full document

... The oscillation of 1.5 has been studied by many authors, the interested reader is referred to the seminal books by Doˇsl ´y and ˇReh´ak 3 and Agarwal et al. 4, 5, where in addition to mainly oscillation ... See full document

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

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

... differential/difference equations has been the object of many researchers over the last ...differential/difference equations of fractional order has drawn significant ...and oscillation of ... See full document

... several oscillation results were established for different kinds of impulsive delay differential equations (see Agarwal and Karakoc ...interval oscillation of impulsive delay ... 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

... that second order neutral functional differential equations have applications in problems dealing with vibrating masses attached to an elastic bar and in some variational ...differential ... 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 ...neutral delay difference ... 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

... 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

... the oscillation theory of dynamic equations on time scales has become one of the research ...of second-order nonlinear delay dynamic equation ... 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

... 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

... A time scale T is an arbitrary nonempty closed subset of the real numbers. The theory of time scales was introduced by Hilger [6] in his Ph.D. thesis in 1988 in order to unify continuous and discrete analysis. ... 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

... in order to unify the continuous and discrete analysis, has received significant ...the oscillation and nonoscillation of solutions of various equations on time scales; we refer the reader to the ... See full document