Abstract
The oscillation of differential equations plays an important role in many applications in physics, biology and engineering. The symmetry helps to deciding the right way to study oscillatory behavior of solutions of this equations. The purpose of this article is to establish new oscillatory properties which describe both the necessary and sufficient conditions for a class of nonlinear second-order differential equations with neutral term and mixed delays of the form (p(iota)(w'(iota)(alpha))' + r(iota)u(beta)(nu(iota)) = 0, iota >= iota(0) where w(iota) = u(iota) + q(iota)u(zeta(iota)). Furthermore, examining the validity of the proposed criteria has been demonstrated via particular examples.