Opial's type inequalities on time scales and some applications
We prove some new Opial type inequalities on time scales and employ them to prove several results related to the spacing between consecutive zeros of a solution or between a zero of a solution and a zero of its derivative for second order dynamic equations on time scales. We also apply these inequalities to obtain a lower bound for the smallest eigenvalue of a Sturm-Liouville eigenvalue problem on time scales. The results contain as special cases some results obtained for second order differential...