Distribution of zeros of solutions of self-adjoint fourth order differential equations

In this paper, for self-adjoint fourth order differential equations, we establish some lower bounds on the distance between zeros of a nontrivial solution and also lower bounds on the distance between zeros of a solution and/or its derivatives. We also give new results related to boundary value problems which arise in the bending of rods. The main results will be proved by making use of some generalizations of Hardy, Opial and Wirtinger type inequalities.