Dynamic Systems and Applications 15 (2006) 629-644 OSCILLATION OF SECOND-ORDER NEUTRAL DELAY DYNAMIC EQUATIONS OF EMDEN-FOWLER TYPE
نویسنده
چکیده
In this paper, we will establish some new oscillation criteria for the second-order superlinear neutral delay dynamic equation of Emden-Fowler type [ a(t)(y(t) + r(t)y(τ(t))) ]∆ + p(t) |y(δ(t))| signy(δ(t)) = 0, on a time scale T; here γ > 1, a(t), r(t), τ(t), p(t) and δ(t)real-valued positive functions defined on T. Our results in the special case when T = R, improve the oscillation results for superlinear neutral delay differential equations and are essentially new on the other different types of time scales. We illustrate the main results by some examples. To the best of our knowledge nothing is known regarding the qualitative behavior of these equations on time scales, so this paper initiates the study of these equations. AMS (MOS) Subject Classification. 34K11, 39A10, 39A99 (34A99, 34C10, 39A11).
منابع مشابه
Oscillation for a Class of Second-Order Emden-Fowler Delay Dynamic Equations on Time Scales
By means of Riccati transformation technique, we establish some new oscillation criteria for the second-order Emden-Fowler delay dynamic equations rxΔ Δ t p t x τ t 0 on a time scale T; here γ is a quotient of odd positive integers with r and p as real-valued positive rd-continuous functions defined on T. Our results in this paper not only extend the results given in Agarwal et al. 2005 , Akin-...
متن کاملOscillation Behavior of Third-Order Neutral Emden-Fowler Delay Dynamic Equations on Time Scales
Wewill establish some oscillation criteria for the third-order Emden-Fowler neutral delay dynamic equations r t x t − a t x τ t ΔΔ Δ p t x δ t 0 on a time scale T, where γ > 0 is a quotient of odd positive integers with r, a, and p real-valued positive rd-continuous functions defined on T. To the best of our knowledge nothing is known regarding the qualitative behavior of these equations on tim...
متن کاملOscillation of Damped Second Order Nonlinear Delay Differential Equations of Emden–Fowler Type
In this paper we establish some new oscillation criteria for a second order nonlinear delay differential equation of Emden–Fowler type with damping term. These results extend and improve some of the well-known results in the nondelay case. Our results in the delay case are new and can be applied to new classes of equations which are not covered by the known criteria for oscillation. Some select...
متن کاملOscillation of second-order Emden–Fowler neutral delay differential equations
We establish some new criteria for the oscillation of second-order Emden–Fowler neutral delay differential equations.We study the case of superlinear and the case of sublinear equations subject to various conditions. The results obtained show that the presence of a neutral term in a differential equation can cause or destroy oscillatory properties. Several examples are provided to illustrate th...
متن کاملOscillation and asymptotic properties of a class of second-order Emden–Fowler neutral differential equations
We consider a class of second-order Emden-Fowler equations with positive and nonpositve neutral coefficients. By using the Riccati transformation and inequalities, several oscillation and asymptotic results are established. Some examples are given to illustrate the main results.
متن کامل