Oscillation criteria for second-order neutral equations with distributed deviating arguments

Oscillation of second order neutral equations with distributed deviating argument

Oscillation criteria are established for the second order neutral delay differential equation with distributed deviating argument (r(t) (x(t))Z′(t))′ + ∫ b a q(t, )f [x(g(t, ))] d ( )= 0, t t0, where Z(t)= x(t)+p(t)x(t − ). These results are extensions of the integral averaging techniques due to Coles and Kamenev, and improve some known oscillation criteria in the existing literature. © 2006 El...

Oscillation of Second-order Quasi-linear Neutral Functional Dynamic Equations with Distributed Deviating Arguments

In this paper, some sufficient conditions for the oscillation of second-order nonlinear neutral functional dynamic equation ( r(t) ( [x(t) + p(t)x[τ(t)]] )γ)∆ + ∫ b a q(t, ξ)x [g(t, ξ)]∆ξ = 0, t ∈ T are established. An example is given to illustrate an application of our results.

Oscillation criteria for second-order neutral equations with distributed deviating argument

Oscillation Criteria for Damping Quasi-Linear Neutral Differential Equations with Distributed Deviating Arguments

In this paper, we investigate the oscillation criteria for damp quasi-linear neutral differential equations with distributed deviating arguments. By using the generalized Riccati transformation and integral averaging, several new criteria that ensure the oscillation of solutions are obtained. Our results not only include some previously known results, but apply to some damped differential equat...

Oscillation Theorems for Even Order Neutral Equations with Continuous Distributed Deviating Arguments

A class of even order neutral equations with continuous distributed deviating arguments [x(t) + ∫ d c p(t, η)x[r(t, η)]dτ(η)] + ∫ b a q(t, ξ)f(x[g(t, ξ)])dσ(ξ) = 0 is considered and its oscillation theorems are discussed. These theorems are of higher degree of generality and deal with the cases which are not covered by the known criteria. Particularly, these criteria extend and unify a number o...