OSCILLATION BEHAVIOR OF SECOND ORDER NONLINEAR NEUTRAL DIFFERENTIAL EQUATIONS WITH DEVIATING ARGUMENTS

Abstract. Oscillation criteria are established for second order nonlinear neutral differential equations with deviating arguments of the form r(t)ψ(x(t)) ∣∣z′(t)∣∣α−1 z′(t) + b∫ a q(t, ξ)f(x(g(t, ψ)))dσ(ξ) = 0, t ≥ t0, where α> 0 and z(t) = x(t) + p(t)x(t − τ). Our results improve and extend some known results in the literature. Some illustrating examples are also provided to show the importance of our results