The distance between zeros of an oscillatory solution to a half-linear differential equation

Consider the oscillatory equation (|u′(t)′α−1u′(t))′+q(t)|u(t)|α−1u(t)=0 where q(t) : [a, ∞) → R is locally integrable for some a ≥ 0. We prove some results on the distance between consecutive zeros of a solution of (∗). We apply also the results to the following equations: (r(t)|u′(t)|α−1u′(t))′+q(t)|u(t)|α−1u(t)=0 and ∑i=1NDi(|Du|n−2Diu)+c(|x|)|u|n−2u=0, ξ∈ωa , where (i)r∈C([0,∞),(0,∞)) and ∫∞ar(t)−1α=∞ (ii) Di = δδxi, D = (D1,…,DN); Щa = x ϵ RN : ¦x¦ ≥ a is an exterior domain, and c ϵ C([a, ∞), [0, ∞)) ; (iii)α>0;n>1 and N⩾2 .