Oscillation of even order nonlinear delay dynamic equations on time scales

Properties of third-order nonlinear delay dynamic equations with positive and negative coefficients

“…Agarwal et al [1] studied oscillation of second-order dynamic equations and turned to the nonexistence of eventually positive solutions of a first-order dynamic inequality. Grace et al [13] and Erbe et al [9] investigated the oscillation of higher order dynamic equations to make a comparison with second-order dynamic equations and dynamic inequalities respectively. Jozef et al [7] also used the comparison method to study the oscillatory properties of (1.1) when T = R, and then, in 2017, they [2] continued the investigation to study nonoscillation properties of (1.1).…”

Oscillation of higher-order neutral dynamic equations on time scales

“…We will also use the time scale version of a lemma due to Onose [15] for T = R. The result here is for an arbitrary time scale and since the proof of this result is similar to the proof of Lemma 2.4 in Erbe et al [14] we state it without proof. Lemma 2.4.…”

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].…”