Second-order Neutral Delay Dynamic Equations Research Articles

New oscillation criteria and some refinements for second-order neutral delay dynamic equations on time scales

In this paper, we present more effective criteria for oscillation of second-order half-linear neutral dynamic equations with delayed arguments. Our results essentially improve, complement, and simplify several related ones in the literature. Some examples are given to illustrate our main results.

New oscillation criteria for second-order neutral delay dynamic equations with a non-positive neutral term on time scales

In this paper, we investigate the oscillatory behavior of solutions of a class of secondorder nonlinear neutral delay dynamic equations with non-positive coefficient where α ≥ β are ratios of odd positive integers and z(t) := x(t) - p(t)x(τ (t)). The obtained results guarantee that all solutions are oscillatory. Illustrative examples are provided.

New Oscillation Criteria for Second-Order Neutral Delay Dynamic Equations with a Nonpositive Neutral Term on Time Scales

New Oscillation Criteria for Second-Order Neutral Delay Dynamic Equations with a Nonpositive Neutral Term on Time Scales

New oscillation criteria for second-order neutral delay dynamic equations

New oscillation criteria for second-order neutral delay dynamic equations

A Philos-type theorem for second-order neutral delay dynamic equations with damping

We establish a Philos-type oscillation theorem for a class of nonlinear second-order neutral delay dynamic equations with damping on a time scale by using the Riccati transformation and integral averaging technique. An illustrative example is provided to show that our theorem has practicability and maneuverability.

On the Oscillation of Second-Order Nonlinear Neutral Delay Dynamic Equations on Time Scales

Based on Riccati transformation and the inequality technique, we establish some new sufficient conditions for oscillation of the second-order neutral delay dynamic equations on time scales. Our results not only extend and improve some known theorems, but also unify the oscillation of the second-order nonlinear delay differential equation and the second-order nonlinear delay difference equation on time scales. At the end of this paper, we give an example to illustrate the main results.

Classification and Existence of Nonoscillatory Solutions of the Second-Order Neutral Delay Dynamic Equations on Time Scales

In the present paper, we give a classification of nonoscillatory solutions of the second-order neutral delay dynamic equation on time scales $$ \begin{array}{*{20}{c}} {{{{\left[ {x(t)-c(t)x\left( {t-\tau } \right)} \right]}}^{{\varDelta \varDelta }}}+f\left( {t,x\left( {{g_1}(t)} \right),\ldots,x\left( {{g_m}(t)} \right)} \right)=0,} \hfill & {t\in T.} \hfill \end{array} $$ Some existence results for each kind of nonoscillatory solutions are also established.

Asymptotic behavior of second-order nonlinear neutral dynamic equations

Abstract This paper is concerned with oscillation and asymptotic behavior of a second-order neutral delay dynamic equation on an arbitrary time scale. We obtain two theorems which guarantee that every solution of the studied equation oscillates or converges to zero. These results improve and complement some known results given in the literature. MSC:34K11, 34N05, 39A10, 39A12, 39A13, 39A21.

Oscillation Criteria for Second-Order Neutral Delay Dynamic Equations with Nonlinearities Given by Riemann-Stieltjes Integrals

We establish several oscillation criteria for a class of second-order neutral delay dynamic equations with nonlinearities given by Riemann-Stieltjes integrals. Our results extend and unify a number of other existing results and handle the cases which are not covered by known criteria. The new results we obtain are of significance because the equations we study allow an infinite number of nonlinear terms and even a continuum of nonlinearities.

New oscillation results for second-order neutral delay dynamic equations

Abstract This paper is concerned with oscillatory behavior of a certain class of second-order neutral delay dynamic equations ( r ( t ) [ x ( t ) + p ( t ) x ( τ ( t ) ) ] Δ ) Δ + q ( t ) x ( δ ( t ) ) = 0 , on a time scale T with sup T = ∞ , where 0 ≤ p ( t ) ≤ p 0 < ∞ . Some new results are presented that not only complement and improve those related results in the literature, but also improve some known results for a second-order delay dynamic equation without a neutral term. Further, the main results improve some related results for second-order neutral differential equations. MSC:34K11, 34N05, 39A10.

Oscillation Criteria for Second-Order Neutral Delay Dynamic Equations with Mixed Nonlinearities

This paper is concerned with some oscillation criteria for the second order neutral delay dynamic equations with mixed nonlinearities of the form where and with . Further the results obtained here generalize and complement to the results obtained by Han et al. (2010). Examples are provided to illustrate the results.

Existence of Nonoscillatory Solutions to Second-Order Neutral Delay Dynamic Equations on Time Scales

We employ Kranoselskii's fixed point theorem to establish the existence of nonoscillatory solutions to the second-order neutral delay dynamic equation on a time scale T. To dwell upon the importance of our results, one interesting example is also included.