Oscillation Criteria for Even Order Neutral Equations with Distributed Deviating Argument

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 criteria for second-order neutral equations with distributed deviating argument

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...

Oscillation Criteria for Certain Even Order Differential Equations with Distributed Deviating Arguments

By using averaging function and the approach developed by Philos and Kong, Kamenevtype and interval oscillation criteria are established for the even order differential equation with distributed deviating arguments, (r(t)|x(n−1)(t)|p−1x(n−1)(t))′ + β ∫ α F [t,ξ ,x(g(t,ξ ))]dσ(ξ ) = 0. The obtained results are extensions of existing ones for second order linear differential equations. Mathematic...

Oscillation criteria for even-order neutral differential equations

Our aim in this paper is to present sufficient conditions for the oscillation of the second order neutral differential equation ( x(t)− px(t− τ ))′′ + q(t)x(σ(t)) = 0.