Oscillation criteria for higher order quasilinear dynamic equations with Laplacians and a deviating argument

Oscillation for Third-Order Nonlinear Differential Equations with Deviating Argument

and Applied Analysis 3 If any solution x of 1.1 is either oscillatory, or satisfies the condition 1.7 , or admits the asymptotic representation x i c 1 sin t − α i εi t , i 0, 1, 2, 3 , 1.8 where c / 0 and α are constants, the continuous functions εi i 0, 1, 2, 3 vanish at infinity and ε0 satisfies the inequality cε0 t > 0 for large t, then we say that 1.1 has weak property A. For n 3, the resu...

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

Kamenev-type Oscillation Criteria for Second-order Quasilinear Differential Equations

We obtain Kamenev-type oscillation criteria for the second-order quasilinear differential equation (r(t)|y′(t)|α−1y′(t))′ + p(t)|y(t)|β−1y(t) = 0 . The criteria obtained extend the integral averaging technique and include earlier results due to Kamenev, Philos and Wong.

Oscillation Criteria for a Certain Second-order Nonlinear Differential Equations with Deviating Arguments

In this paper, by using the generalized Riccati technique and the integral averaging technique, some new oscillation criteria for certain second order retarded differential equation of the form