Order Neutral Dynamic Equations Research Articles

Fourth-order neutral dynamic equations oscillate on timescales with different arguments

<p>The theory of neutral dynamic equations on timescales was based to unify the study of differential and difference equations. The article described several oscillating criteria that will be developed for fourth-order-neutral dynamic equations in the presence of various types of arguments on timescales. The goal was to establish all necessary conditions for the solutions of these models to be oscillatory. To construct observation values, ideas from [Y. Sui and Z. Han, Oscillation of second order neutral dynamic equations with deviating arguments on time scales, <italic>Adv. Differ. Equ.</italic>, 10 (2018)] were used. The research seeked to provide sufficient criteria that ensured the oscillation of solutions to these complex dynamic equations using a technique Riccati transformations generalized, emphasizing their importance in the study of oscillatory processes within various scientific and engineering contexts.</p>

Oscillatory properties of third order neutral dynamic equations

Oscillatory properties of third-order half-linear neutral dynamic equations were investigated in this paper. Some conditions are obtained to ensure the oscillation of all solutions of a neutral dynamic equation with several coefficients and several variable delays, t ∈ [t0, ∞)\U0001d54b, where γ > 0 is a quotient of odd positive integers, , and , and the results are supported by illustrative examples.

Oscillation Properties of Solutions of Second Order Neutral Dynamic Equations of Non-canonical Type on Time Scales

Oscillation Properties of Solutions of Second Order Neutral Dynamic Equations of Non-canonical Type on Time Scales

Oscillation theorems for second order neutral dynamic equations with maxima and mixed arguments on time scales

In this work, we establish new oscillation criteria for the second order neutral dynamic equation with maxima and mixed arguments of the form: where New comparison theorems are obtained that allow us to examine the oscillation of the given second order dynamic equation by examining the oscillatory behavior of first order dynamic ones. The obtained results extend and complement some known ones in literature. Examples are given to illustrate the importance of our results.

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.

Oscillation of second order neutral dynamic equations with deviating arguments on time scales

In this paper, we consider the following second order neutral dynamic equations with deviating arguments on time scales: \t\t\t(r(t)(zΔ(t))α)Δ+q(t)f(y(m(t)))=0,\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$\\bigl(r(t) \\bigl(z^{\\Delta}(t)\\bigr)^{\\alpha}\\bigr)^{\\Delta}+q(t)f \\bigl(y\\bigl(m(t)\\bigr)\\bigr)=0, $$\\end{document} where z(t)=y(t)+p(t)y(tau(t)), m(t)leq t or m(t)geq t, and tau(t)leq t. Some new oscillatory criteria are obtained by means of the inequality technique and a Riccati transformation. Our results extend and improve many well-known results for oscillation of second order dynamic equations. Some examples are given to illustrate the main results.

Oscillation criteria for second order neutral dynamic equations of Emden-Fowler type with positive and negative coefficients on time scales

We investigate oscillation of certain second order neutral dynamic equations of Emden-Fowler type with positive and negative coefficients. We use some different techniques and apply Riccati transformation to establish new oscillatory criteria which include two necessary and sufficient conditions. Moreover, we point out that how the power γ plays its role. Some interesting examples are given to illustrate the versatility of our results.

Oscillation of second order neutral dynamic equations with distributed delay

Oscillation of second order neutral dynamic equations with distributed delay

Oscillatory and asymptotic behaviour of second order neutral dynamic equations with positive and negative coefficients

Oscillatory and asymptotic behaviour of second order neutral dynamic equations with positive and negative coefficients

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 Second-Order Neutral Dynamic Equations with Mixed Arguments

We present some new oscillation criteria for a class of half-linear second -order neutral dynamic equations with mixed arguments. An example is given to illustrate the main results.

Oscillation and nonoscillation for second order neutral dynamic equations with positive and negative coefficients on time scales

Abstract We investigate oscillation and nonoscillation of certain second order neutral dynamic equations with positive and negative coefficients. We apply the results from the theory of lower and upper solutions for related dynamic equations along with some additional estimates on positive solutions and use different techniques to obtain some oscillatory theorems. Also, we apply Kranoselskii’s fixed point theorem to obtain nonoscillatory results and then give two sufficient and necessary conditions for the equations to be oscillatory. Some interesting examples are given to illustrate the versatility of our 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.