Oscillation for higher order differential equations with a middle term

Hence, q is bounded from above and limt→∞ q(t) = q∞ <∞. Note that the function r may change sign. By a solution of () we mean a function x differentiable up to order n which satisfies () on [Tx,∞), Tx ≥ . A solution of () is said to be proper if sup{|x(t)| : t ≥ T} >  for any T ≥ Tx. As usual, a solution x of () is said to be oscillatory if x changes sign for large t. The aim of this paper is to study () as a perturbation of the linear differential equation