A New Oscillation Criterion for Forced Second-Order Quasilinear Differential Equations

where p, q, e ∈ C t0,∞ , with p t > 0 and 0 < α ≤ β being constants. By a solution of 1.1 , wemean a function y t ∈ C1 Ty,∞ , , where Ty ≥ t0 depends on the particular solution, which has the property p t |y′ t |α−1y′ t ∈ C1 Ty,∞ and satisfies 1.1 . We restrict our attention to the nontrivial solutions y t of 1.1 only, that is, to solutions y t such that sup{|y t | : t ≥ T} > 0 for all T ≥ Ty . A nontrivial solution of 1.1 is called oscillatory if it has arbitrarily large zeros, otherwise, it is said to be nonoscillatory. Equation 1.1 is said to be oscillatory if all its nontrivial solutions are oscillatory. We note that when 0 < α β, 1.1 turns into the half-linear differential equation