Distributions of Zeros of Solutions for Third-Order Differential Equations with Variable Coefficients

Abstract

For the third-order linear differential equations of the formr(t)x′′(t)′+p(t)x′(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 and some generalizations of Opial and Wirtinger type inequalities.