[PDF] Top 20 Oscillatory and Asymptotic Behavior of Solutions of Second Order Neutral Delay Difference Equations with “Maxima”

... the oscillatory and asymptotic behavior of solutions of neutral difference equations, see [1]-[5], and the references cited ...the oscillatory and asymptotic ... See full document

... every solution of (1.1) is either oscillatory or tends to zero. Proof. Assume the contrary. Without loss of generality, we may suppose that {x(n)} is an eventually positive solution of (1.1) such that lim sup n→∞ ... See full document

... function. For the first one, it is also usual to assume, when dealing with oscillation and nonoscillation, that f (n, · ) is “sign-preserving,” that is, f (n,x) · x ≥ 0 for all n ∈ N and all x ∈ R . The simplest result ... See full document

... differential equations, the theory of the asymptotic behaviour of their solutions has not yet been fully ...particular, asymptotic behavior of solutions of impulsive delay ... See full document

... 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 oscillatory behavior ... See full document

... Recently, neutral delay difference equations, that is, difference equations in which the highest order difference of the unknown sequence appears both with and ... 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 conditions ... See full document

... However, to the best of our knowledge, there does not appear to be any results for the third-order neutral dynamic equations on time scales in the case p(t) ≥ . The main aim of this paper is to ... See full document

... and asymptotic behavior of various classes of second-order and high-order differential equations and dynamic equations on time scales ...(TO) neutral differential and ... See full document

... for second-order non- linear neutral delay difference equations are obtained by means of inequality techniques, specific function sequences and non-increasing solutions for ... See full document

... nonlinear difference equation was studied intensively by ...of oscillatory behavior of solutions of nonlinear neutral delay difference ...fourth order nonlinear ... See full document

... Difference equations occur as mathematical models of some real-world ...of neutral delay difference equations (NDDEs in ...for neutral equations of any order; see [6, ... See full document

... differential equations find numerous applications in natural science and ...the oscillatory behavior of solutions of neutral delay differential equations, and we refer to ... See full document

... of second order difference of any two linear combination of a given ...the asymptotic behavior of sequence under suitable combination of second order functional ...even ... 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

... nonoscillatory solutions for equation ...nonoscillatory solutions and study error estimates between the approximation sequences and the bounded nonoscillatory ... See full document

... In this paper, we have obtained several new oscillation criteria for a second order nonlinear advanced differential equation with mixed neutral terms. Our results improve and com- plement some ... See full document

... The purpose of this paper is to extend the oscillation results given in [] and []. Os- cillation criteria for third-order dynamic equations have recently been studied in [–]. Other papers related with ... See full document

... differential equations to determine the exact asymptotic behavior at infinity of the solutions under the appropriate assumptions for the coefficients of an ...the solutions, as well as ... See full document

... ficulties one encounters lies in the fact that x(t) ≥ ( – p(t))z(t) is not a valid estimate if p(t) >  and x is an eventually positive solution of (.). The question regarding the anal- ysis of oscillatory ... See full document