Belohorec-type Oscillation Theorem for Second Order Sublinear Dynamic Equations on Time Scales

Consider the Emden-Fowler sublinear dynamic equation (0.1) x(t) + p(t)x(σ(t)) = 0, where p ∈ C(T, R), where T is a time scale, 0 < α < 1, α is the quotient of odd positive integers. When p(t) is allowed to take on negative values, we obtain a Belohorec-type oscillation theorem for (0.1). As an application, we get that the sublinear difference equation (0.2) ∆x(n) + p(n)x(n+ 1) = 0, is oscillatory, if ∞ X np(n) =∞, and the sublinear q-difference equation (0.3) x(t) + p(t)x(qt) = 0. where t ∈ qN0 , q > 1, is oscillatory, if Z ∞ 1 tp(t)∆t =∞.