Higher-order Neutral Dynamic Equations Research Articles

Existence of nonoscillatory solutions to nonlinear higher-order neutral dynamic equations

We investigate the existence of different types of nonoscillatory solutions to a class of higher-order nonlinear neutral dynamic equations on a time scale. Two examples are provided to show the significance of the conclusions.

Nonoscillation of higher order neutral dynamic equations on time scales

The purpose of this paper is to prove the existence theorems of the nonoscillatory solution for higher order neutral dynamic equations on time scales. Our results improve and generalize the recent known results by removing some restrictive conditions.

Existence of the nonoscillatory solutions of higher order neutral dynamic equations on time scales

In this paper, we investigate the existence of the nonoscillatory solutions of the following higher order neutral dynamic equation: $\{r_{n}(t)[(r_{n-1}(t)(\cdots(r_{1}(t)(x(t)-q(t)x(\tau(t)))^{\Delta })^{\Delta}\cdots)^{\Delta})^{\Delta}]^{\gamma}\}^{\Delta} +f(t,x(\delta (t)))=0$ for $t\in \left .[t_{0},\infty) \right ._{\mathbb{T}}$ , and obtain some necessary and sufficient conditions for the existence of nonoscillatory bounded solutions for this equation.

Oscillation of higher-order neutral dynamic equations on time scales

In this article, using comparison with second-order dynamic equations, we establish sufficient conditions for oscillatory solutions of an n th-order neutral dynamic equation with distributed deviating arguments. The arguments are based on Taylor monomials on time scales.2000 Mathematics Subject Classification: 34K11; 39A10; 39A99.

Nonoscillatory Solutions for Higher-Order Neutral Dynamic Equations on Time Scales

We study the higher-order neutral dynamic equation{a(t)[(x(t)−p(t)x(τ(t)))Δm]α}Δ+f(t,x(δ(t)))=0fort∈[t0,∞)Tand obtain some necessary and sufficient conditions for the existence of nonoscillatory bounded solutions for this equation.

Asymptotic behaviour of bounded solutions of a class of higher-order neutral dynamic equations

In this paper, necessary and sufficient conditions for the asymptotic behaviour of all bounded solutions of a class of nonlinear higher-order neutral dynamic equations are stated related to various ranges of the coefficient associated with the neutral part, in one of which the coefficient is allowed to oscillate and not tend to zero asymptotically. The new results improve and generalize the known results stated for difference equations and differential equations, and answer some problems left open for the case T = R for arbitrary time scales. Some certain examples, which the results in the literature fail to deliver an answer to, are given to illustrate the applicability and significance of the new results.

Existence of nonoscillatory solutions for higher order neutral dynamic equations on time scales

In this paper, we consider higher order nonlinear neutral dynamic equation on time scales. Some sufficient conditions are obtained for existence of a nonoscillatory solution for the higher order equation by using fixed point theory and defining the compressed injection on a set.