Oscillation of second-order nonlinear delay differential equations with nonpositive neutral coefficients

By a solution to (.), we mean a function x ∈ C([Tx,∞),R), Tx ≥ t which has the property r(z′)α ∈ C([Tx,∞),R) and satisfies (.) on the interval [Tx,∞). We consider only those solutions of (.) which satisfy condition sup{|x(t)| : t ≥ T} >  for all T ≥ Tx and assume that (.) possesses such solutions. As usual, a solution of (.) is called oscillatory if it has arbitrarily large zeros on [Tx,∞); otherwise, it is said to be nonoscillatory. Equation (.) is termed oscillatory if all its solutions oscillate.