Oscillation of Noncanonical Second-Order Advanced Differential Equations via Canonical Transform

In this paper, we develop a new technique to deduce oscillation of a second-order noncanonical advanced differential equation by using established criteria for second-order canonical advanced differential equations. We illustrate our results by presenting two examples

Asymptotic and oscillatory behavior of solutions of a class of second order differential equations with deviating arguments

AbstractThe asymptotic and oscillatory behavior of solutions of damped nonlinear second order differential equations with deviating arguments of the type (a(t) ψ(x(t)) ẋ(t)). + p(t)ẋ(t) + q(t) + q(t)f(x[g(t)]) = 0 (. = d/dt) is studied. Criteria for oscillation of all solutions when the damping coefficient “p” is of constant sign on [t0, ∞) are established. Results on the asymptotic and oscillatory behavior of solutions of the damped-forced equation (a(t)ψ(x(t))ẋ(t)). + p(t)ẋ(t) + q(t)f(x[g(t)]) = e(t), where q is allowed to change signs in [t0, ∞), are also presented. Some of the results of this paper extend, improve, and correlate a number of existing criteria

Asymptotic behavior of solutions of the third-order nonlinear advanced differential equations

The aim of this work is to study some asymptotic properties of a class of third-order advanced differential equations. We present new oscillation criteria that complete, simplify and improve some previous results. We also provide many different examples to clarify the significance of our results

Oscillation of Half-Linear Differential Equations with Delay

We study the half-linear delay differential equation , , We establish a new a priori bound for the nonoscillatory solution of this equation and utilize this bound to derive new oscillation criteria for this equation in terms of oscillation criteria for an ordinary half-linear differential equation. The presented results extend and improve previous results of other authors. An extension to neutral equations is also provided

Oscillatory Behavior of Noncanonical Quasilinear Second-Order Dynamic Equations on Time Scales

The objective of this article is to examine the oscillatory behavior of a class of quasilinear second-order dynamic equations on time scales. Our focus will be on the noncanonical case, which has received relatively less attention compared to the more commonly studied canonical dynamic equations. Our approach involves transforming the noncanonical equation into a corresponding canonical equation. By utilizing this transformation and a range of techniques, we develop new, more efficient, and precise oscillation criteria. Finally, we demonstrate the significance and usefulness of our results by applying them to specific cases within the equation being studied. © 2023 A. Hassan et al

Oscillation of second order neutral dynamic equations with distributed delay

In this paper, we establish new oscillation criteria for second order neutral dynamic equations with distributed delay by employing the generalized Riccati transformation. The obtained theorems essentially improve the oscillation results in the literature. And two examples are provided to illustrate to the versatility of our main results

Improved results for testing the oscillation of functional differential equations with multiple delays

In this article, we test whether solutions of second-order delay functional differential equations oscillate. The considered equation is a general case of several important equations, such as the linear, half-linear, and Emden-Fowler equations. We can construct strict criteria by inferring new qualities from the positive solutions to the problem under study. Furthermore, we can incrementally enhance these characteristics. We can use the criteria more than once if they are unsuccessful the first time thanks to their iterative nature. Sharp criteria were obtained with only one condition that guarantees the oscillation of the equation in the canonical and noncanonical forms. Our oscillation results effectively extend, complete, and simplify several related ones in the literature. An example was given to show the significance of the main results