Lyapunov's Type Inequalities for Fourth-Order Differential Equations

Samir H. Saker

Abstract and Applied Analysis, 2012, vol. 2012, 1-25

Abstract:

For a fourth-order differential equation, we will establish some new Lyapunov-type inequalities, which give lower bounds of the distance between zeros of a nontrivial solution and also lower bounds of 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-Wirtinger-type inequalities involving higher-order derivatives. Some examples are considered to illustrate the main results.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:795825

DOI: 10.1155/2012/795825

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