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For the third-order linear differential equations of the form r ( 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.

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