[PDF] Top 20 Oscillation results for nonlinear second order difference equations with mixed neutral terms

... The rest of the paper is organized as follows: Sect. 2 is devoted to the main results of the paper. We present our investigations in two folds for Eqs. (1) and (2). Meanwhile, a relevant result on the existence of ... See full document

... Advanced differential equations can find applications in a mass of real world problems where the evolution rate depends on present and future values of the quantity. Therefore, taking into account the impact of ... See full document

... interval oscillation criteria were recently extended to second-order dynamic equations in ...Further results on oscillatory and nonoscillatory behavior of the second order ... See full document

... the oscillation of all solutions of a second order difference equation with several super-linear neutral ...The results obtained here extend or complement some of the known ... 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

... the oscillation constant. Other results on the oscillation constant for difference equations can be found in [–] and the references cited ... See full document

... The oscillation theory of difference equations and their applications have been receiving intensive attention in the last few decades, see for example [1, 2, 4], and the references cited ...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

... In this paper, we investigate the asymptotical behavior for a partial sum sequence of independent random variables, and we derive a law of the iterated logarithm type. It is worth to point out that the partial sum ... 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 ... 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

... equation (1.1). A nontrivial solution of equation (1.1) is said to be oscillatory if its terms are neither eventually positive nor eventually negative, and otherwise it is called nonoscillatory. Equation (1.1) is ... 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

... presented oscillation criteria which improved the existing results for the ...the oscillation of all solu- tions of equation ...new oscillation criteria, which improve and complement that ... See full document

... several oscillation criteria for a class of second-order nonlinear neutral differential ...related results reported in the literature and can be used in cases where known theorems ... 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 ...of neutral ... See full document

... Thandapani, Oscillatory and nonoscillatory behavior of second order neutral delay difference equations, Math.. Thandapani, Oscillatory and nonoscillatory behavior of second order neutral[r] ... 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

... some oscillation criteria for the solutions of mth-order nonlinear neutral difference equation where m ≥ ...The results presented here complement some of the known results ... See full document

... If all solutions of Eq. (1.1) are oscillatory, then Eq. (1.1) is said to be oscillatory. Before given the main results, we note that the initial value problem which consists of Eq. (1.1) and the initial function ... See full document