Oscillation Criteria for Some New Generalized Emden-Fowler Dynamic Equations on Time Scales

By means of novel analytical techniques, we have established several new oscillation criteria for the generalized Emden-Fowler dynamic equation on a time scale, that is, (r (t) | ZΔ (t) | α - 1 Z Δ (t)) Δ + f (t, x (δ (t))) = 0, with respect to the case ∫ t 0 ∞ r-1/α (s) Δ s = ∞ and the case ∫t0 ∞ r-1/α (s) Δ s < ∞, where Z (t) = x (t) + p (t) x (τ (t)), α is a constant, | f (t, u) | q (t) | uβ |, β is a constant satisfying α β > 0, and r, p, and q are real valued right-dense continuous nonnegative functions defined on. Noting the parameter value α probably unequal to β, our equation factually includes the existing models as special cases; our results are more general and have wider adaptive range than others' work in the literature. © 2013 Haidong Liu and Puchen Liu.