Gaps between zeros of solutions for a certain class of third-order differential equations

Abstract In this paper, we establish some lower bounds for the distance between zeros of nontrivial solutions or/and their derivatives and extend some results about distribution of zeros for a certain class of third-order differential equations of the form (r2(t)(r1(t)x′(t))′)′+p(t)x′(t)+q(t)x(t)=0. The main results of this paper will be proved by employing some Hardy’s and Opial’s type inequalities