Oscillation Criteria for Solutions to Nonlinear Dynamic Equations of Higher Order

Abstract

In this paper using some new dynamic inequalities we present some oscillation results for higher order dynamic equationon an unbounded time scale T. Some new oscillation criteria are obtained using comparison techniques. Some applications illustrating our results are included.

Kamenev-Type Criteria for Testing the Asymptotic Behavior of Solutions of Third-Order Quasi-Linear Neutral Differential Equations

“…Whereas [23][24][25] dealt with damping equations, and [26][27][28][29] studied mixed equations. Over the past 20 years, functional dynamic equations have also drawn a lot of attention; see, for instance, [30][31][32].…”

Oscillation criteria for higher‐order nonlinear dynamic equations with Laplacians and a deviating argument on time scales

“…Recently, using Riccati substitution, Hassan and Kong obtained asymptotics and oscillation criteria for the n th‐order half‐linear dynamic equation with deviating argument where α [1, n − 1]: = α 1 ⋯ α n − 1 ; and Grace and Hassan further studied the asymptotics and oscillation for the higher‐order nonlinear dynamic equation with Laplacians and deviating argument However, the establishment of the results in requires the restriction on the time scale that g ∗ ∘ σ = σ ∘ g ∗ with , which is hardly satisfied, see conclusion 1 in for such a special case. For more results on dynamic equations, we refer the reader to the papers .…”

“…However, the establishment of the results in [8] requires the restriction on the time scale T that g ı D ı g with g .t/ :D minft, g.t/g, which is hardly satisfied, see conclusion 1 in [9] for such a special case. For more results on dynamic equations, we refer the reader to the papers [5,6,[10][11][12][13][14][15][16][17][18][19].…”