The distribution of zeros of solutions for a class of third order differential equation

For third order linear differential equations of the form (r(t)x0 (t))00 + p(t)x0 (t) + q(t)x(t) = 0, we will establish lower bounds for the distance between zeros of a solution and/or its derivatives. The main results will be proved by making use of Hardy's inequality, some generalizations of Opial's inequality and Boyd's inequality.