Oscillation Criteria for Second-Order Delay Dynamic Equations on Time Scales

Abstract

By means of Riccati transformation technique, we establish some new oscillation criteria for the second-order nonlinear delay dynamic equations (p(t)(= 0 on a time scale T, here γ ≥ 1 is a quotient of odd positive integers with p and q realvalued positive rd-continuous functions defined on T.

Oscillation criteria for quasi-linear functional dynamic equations on time scales

“…The main results are proved in Section 2, which is organized as follows: In the subsection 2.1 we consider the case when τ (t) > t and in the subsection 2.2, we consider the case when τ (t) ≤ t. The results in this paper are different from the results established in [21] even in the case when τ (t) = t and can be applied to the equation (1.1) when 0 < γ < 1 and τ (t) > t. The results improve the results established in [1,14,15,19,29,22], in the sense that the results do not require the conditions (1.8), (1.11), (1.13) and r ∆ (t) ≥ 0. The results also can applied on any time scale not only on discrete time scales when µ(t) = 0, which is the case considered in [8].…”

“…Erbe et al [15] considered the half-linear delay dynamic equation (1.12) on time scales, where 0 < γ ≤ 1 is the quotient of odd positive integers and established some sufficient conditions for oscillation when (1.13) holds. Han et al [22] considered (1.12) and followed the proof that has been used in [29] and established some sufficient conditions for oscillation when r ∆ (t) ≥ 0. For oscillation of quasi-linear dynamic equations, Grace et al [21] considered the equation…”

Oscillation of second-order quasi-linear neutral functional dynamic equations with distributed deviating arguments

“…Recently, there has been much research activity concerning the oscillation and non-oscillation of solutions of various dynamic equations on time scales, e.g., see [2,[6][7][8][9][10][11][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29] and the references cited therein. Agarwal et al [2], Saker [18], Tripathy [26] established some oscillation criteria for second-order nonlinear neutral delay dynamic equation…”

“…Han et al [10] and Saker et al [24] examined the oscillation of (1.3) when γ = 1. In particular, Han et al [10] investigated the case where γ = 1 and…”

The Effect of in-Flight Mass Depletion on Bird Migration Range

“…Motivated by the work in [1,23,17,12,18,7] mentioned above, using Riccati type transformations we establish some sufficient conditions guaranteeing the oscillation of solutions of Eq. (1).…”