Nonoscillation criteria for second-order half-linear differential equations

AbstractTwo nonoscillatory characterizations of solutions of the half-linear second-order differential equation of the form [p(t)|y′|α−1y′]′ + q(t)|y|α−1y = 0, a > 0 are established for π(t0 ≔ ∫t0∞ (p(s))−1αds < ∞, and π(t0) = ∞, respectively. Using these results, we obtain some sufficient conditions for all solutions of the above equation to be oscillatory (nonoscillatory)