NEW OSCILLATION CRITERIA FOR GENERALIZED SECOND-ORDER NONLINEAR NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS

In this paper, the authors consider the second-order neutral functional differential equation

           [ p(t) ψ( y(t) )(x′(t) )^γ ] ′ + q(t) f( y(δ(t)) ) = 0,   t ≥ t₀,

where   x(t) = y(t) + r(t) y( τ(t) )  and  γ > 0  is a ratio of odd positive integers. They establish some new sufficient conditions for oscillation of all solutions that are substantial improvements to some existing results in the literature. Some examples are included to illustrate the main results.