Some Oscillation Criteria For First Order Delay Dynamic Equations
نویسنده
چکیده
We present an oscillation criterion for first order delay dynamic equations on time scales, which contains well-known criteria for delay differential equations and delay difference equations as special cases. We illustrate our results by applying them to various kinds of time scales.
منابع مشابه
Oscillation Criteria for Second-Order Quasilinear Neutral Delay Dynamic Equations on Time Scales
We establish some new oscillation criteria for the second-order quasilinear neutral delay dynamic equations r t zΔ t γ Δ q1 t x τ1 t q2 t x τ2 t 0 on a time scale T, where z t x t p t x τ0 t , 0 < α < γ < β. Our results generalize and improve some known results for oscillation of second-order nonlinear delay dynamic equations on time scales. Some examples are considered to illustrate our main r...
متن کاملKamenev-Type Oscillation Criteria for Higher-Order Neutral Delay Dynamic Equations
In this paper, we are primarily concerned with the oscillation of solutions to higher-order dynamic equations. We first extend some recent results which have been obtained for second-order dynamic equations to even-order neutral delay dynamic equations. Our technique depends on making use of the Riccati substitution and the use of properties of the generalized Taylor monomials on time scales. W...
متن کاملOscillation theorems for certain third order nonlinear delay dynamic equations on time scales
In this paper, we establish some new oscillation criteria for the third order nonlinear delay dynamic equations
متن کاملOscillation Criteria for Third-order Nonlinear Delay Dynamic Equations on Time Scales
By means of Riccati transformation technique, we establish some new oscillation criteria for the third-order nonlinear delay dynamic equations x 3 (t) + p(t)x(τ(t)) = 0 on a time scale T unbounded above, here γ > 0 is a quotient of odd positive integers with p real-valued positive rd-continuous function defined on T. Three examples are given to illustrate the main results.
متن کاملOscillation criteria for nonlinear damped dynamic equations on time scales
We present new oscillation criteria for the second order nonlinear damped delay dynamic equation (r(t)(x(t))) + p(t)(x(t)) + q(t)f (x(τ(t))) = 0. Our results generalize and improve some known results for oscillation of second order nonlinear delay dynamic equation. Our results are illustrated with examples.
متن کامل