Lyapunov inequalities for dynamic equations via new Opial type inequalities

Year 2018, Volume: 47 Issue: 6, 1537 - 1551, 12.12.2018

S. H. Saker M. M. Osman D. O'regan R. P. Agarwal

Abstract

In this paper, we prove some new dynamic inequalities of Opial type on time scales. By employing these new inequalities we establish some new Lyapunov type inequalities for a second order dynamic equation with a damping term. These new Lyapunov inequalities give lower bounds on the distance between zeros of a solution and/or its derivative.

Keywords

Disfocality, Opial's inequality, Lyapunov inequality, dynamic equations, time scales

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