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 , where (i)r C([0,∞),(0,∞)) and ∫∞ar(t)−1/α=∞ (ii) , 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.