APPLICATIONS OF OPIAL AND WIRTINGER INEQUALITIES ON ZEROS OF THIRD ORDER DIFFERENTIAL EQUATIONS

In this paper, for a third order differential equation, we will establish some new inequalities of Lyapunov type. These inequalities give implicit lower bounds on the distance between zeros of a nontrivial solution and also lower bounds for the spacing between zeros of a solution and/or its derivatives. The main results will be proved by making use of the H¨older inequality and some generalizations of Opial and Wirtinger type inequalities. Some examples are considered to illustrate the main results.