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

Authors : Samir. H. SAKER, Ramy. R. MAHMOUD

Pages : 455-471

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Publication Date : 2016-04-01

Article Type : Research Paper

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, Opials inequality, Sublinear dynamic equations, Time Scales