Distribution of zeros of sublinear dynamic equations with a damping term on time scales

Year 2016, Volume: 45 Issue: 2, 455 - 471, 01.04.2016

Samir. H. Saker Ramy. R. Mahmoud

Abstract

In this paper, for a second order sublinear dynamic equation with a
damping term we will study the lower bounds of the distance between
zeros of a solution and/or its derivatives and then establish some new
criteria for disconjugacy and disfocality. Our results present a slight
improvement to some results proved in the litrature. As a special case
when T = R, for a second order linear differential equation, we get some
results proved by Brown and Harris as a consequence of our results. The
results will be proved by employing the time scales Hölder inequality,
the time scales chain rule and some new dynamic Opial-type inequalities
designed and proved for this purpose. 

Keywords

Disconjugacy, Disfocality, Lyapunov inequality, Opial’s inequality, Sublinear dynamic equations, Time Scales

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