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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