Oscillation theorems for second-order half-linear differential equations

Oscillation criteria for the second-order half-linear differential equation

r(t)|ξ′(t)|^?1 ξ′(t)]′ + p(t)|ξ(t)|^?1ξ(t)=0, t t₀

are established, where > 0 is a constant and exists for t t₀, ∞). We apply these results to the following equation:

where , D = (D₁,…, D_N), Ω_a = x ^N : |x| ≥ a} is an exterior domain, and c C(a, ∞), ), n > 1 and N ≥ 2 are integers. Here, a > 0 is a given constant.