Oscillatory Behavior of Euler Type Delay Dynamic Equations withp-Laplacian Like Operators

We consider the Euler type delay dynamic equation withp-Laplacin like operators $ (x^{{^{\Delta } }} (v)|x^{{^{\Delta } }} (v)|^{{p - 2}} )^{{^{\Delta } }} + a(v)x^{{^{\Delta } }} (v)|^{{p - 2}} + r(v)x(\delta (v))|x(\delta (v))|^{{p - 2}} = 0 $ , where $ v \in [v_{0} ,\infty ) $ By using new inequality technique, we give some new criteria, which complement related contributions results.

Oscillation criteria for higher order nonlinear delay dynamic equations on time scales

In this paper, we study the oscillation criteria of the following higher order nonlinear delay dynamic equationon an arbitrary time scalewith

Oscillation behavior of third-order quasilinear neutral delay dynamic equations on time scales

The aim of this paper is to give oscillation criteria for the third-order quasilinear neutral delay dynamic equation [r(t)([x(t)+ p(t)x(?0(t))]??)?]? + q1(t)x?(?1(t)) + q2(t)x?(?2(t)) = 0; on a time scale T, where 0 < ? < ? < ?. By using a generalized Riccati transformation and integral averaging technique, we establish some new sufficient conditions which ensure that every solution of this equation oscillates or converges to zero.

Qualitative Analysis of Solutions of Nonlinear Delay Dynamic Equations

We use the fixed point theory to investigate the qualitative analysis of a nonlinear delay dynamic equation on an arbitrary time scales. We illustrate our results by applying them to various kind of time scales.

On the Oscillation of Second Order Nonlinear Neutral Delay Dynamic Equations

In this paper we obtain some new oscillation criteria for the second order nonlinear neutral delay dynamic equation (𝑥(𝑡) – 𝑝(𝑡)𝑥(𝑡 – τ 1))ΔΔ + 𝑞(𝑡)𝑓(𝑥(𝑡 – τ 2)) = 0, on a time scale 𝕋. Moreover, a new sufficient condition for the oscillation sublinear equation (𝑥(𝑡) – 𝑝(𝑡)𝑥(𝑡 – τ 1))″ + 𝑞(𝑡)𝑓(𝑥(𝑡 – τ 2)) = 0, is presented, which improves other conditions and an example is given to illustrate our result.