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Displaying similar documents to “On the inequality of Mathieu.”

Lyapunov type inequalities for a second order differential equation with a damping term

S. H. Saker (2012)

Annales Polonici Mathematici

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For a second order differential equation with a damping term, we 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 derivative. We also obtain a lower bound for the first eigenvalue of a boundary value problem. The main results are proved by applying the Hölder inequality and some generalizations of Opial and...