Oscillation Criteria of Kneser-Hille Type for Second-Order Differential Equations with Nonlinear Perturbed Terms

This paper is concerned with the oscillation problem for nonlinear differential equations of Euler type, which are denoted by (En) with n = 1, 2, 3, . . . . Equation (En) consists of a linear main term and a nonlinear perturbed term. If the nonlinear perturbation vanishes, then all nontrivial solutions of (En) are nonoscillatory. A pair of sufficient and necessary conditions on the perturbed term for all nonlinear solutions of (En) to be oscillatory is given. It is also proved that all solutions of (En) tend to zero.