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

Abstract EN

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-1ZΔ(t))Δ+f(t,x(δ(t)))=0, with respect to the case ∫t0∞r-1/α(s)Δs=∞ and the case ∫t0∞r-1/α(s)Δs<∞, 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.