Lyapunov inequalities for dynamic equations via new Opial type inequalities

Authors : S. H. SAKER, M. M. OSMAN, D. O`REGAN, R. P. AGARWAL

Pages : 1537-1551

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Publication Date : 2018-12-12

Article Type : Research Paper

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